I think I come here overrated, but I probably have some experience doing this very thing with slightly modified numbers.
My truck was a 39 Dodge and I put it on a 92 Dakota chassis. Its unfortunate that I lost all my build pictures in my last computer crash.
Strip you Dakota frame down to a rolling chassis, that will make it easier to fit things.

My chassis was a standard cab, long box. I shortened the wheel base 8" just behind the original box to channel change over on the Dakota. I added the removed piece to the inside of the frame at the splice to box in and reinforce the change over splice and also cover my joint. After the cab was mounted and the radiator support was positioned, I did cut the front end off both front frame rails at the spring pockets and I fabricated new frame horns. (I'm running open wheels and have a modified lower grille, so much of these frame horn modifications were for looks. I never attempted to fit the lower grille piece, so what needs to be done to do that I can't help with).

If you intend to run front fenders, (my truck was built so fenders could be added) it is important that you match up the fender wheel openings with the front wheels on the Dakota chassis. The under hood space for a V8 in the 39-47 under hood space is very tight, everything has to be positioned correctly. I cut the cab's firewall the width of the motor with manifolds, and moved it back to being flush with the original cab indentation. You have to set the firewall cut back high enough to clear the valve covers (and their possible removal) somewhere around 8" from the top of the original cab firewall. The truck is not here to take an actual measurement. The open space in the firewall needs to be enclosed. On my cab, the cowl vent still functions, but I did have to modify the vent lift arm.

As you are preparing to mount your cab, keep in mind the wheel well opening in the front fenders, when bolted in place will determine the cab position on the frame. I actually set my cab where I thought it needed to be, positioned the radiator surround, tightened the radiator surround to cab tie bolts and placed the hood in place before I marked the cab mount locations! I have a 5.9 Magnum V8 in my truck, the back of the motor sits within an inch of the firewall, and I had to move the radiator into the nose piece the full radiator thickness. I'm running the factory serpentine belt system with the waterpump mounted fan with 1" radiator clearance. It really is that close, Ill post pictures.

You will need to remove the original cab mount brackets from the frame because they are in the wrong location for the 39-47 cab. I built new brackets and mounted the 39 cab with the cab floors the same distance off the frame the Dakota cab was mounted. I used 1" thick poly cab mount bushings between the cab and the cab mounts. You may have to adjust the thickness of the body mounts, depending on your ground clearance of the front fenders. Center the cab on the frame rails. Positioning of the cab is critical, tacking the cab mounts in position then weld fully later, after you know everything fits, is the advice I give you.

My cab actually still had decent floors, but I ended up cutting everything in front of the seat riser out between the cab rockers. By the time you flatten the firewall even with the original firewall indent, and box the sides back in (don't do that until the brake booster and steering column are in place), not enough of the original floors exist to be structurally sound because of the piece of wood in the original cab floor. You also will be cutting the floor's center to clear the transmission, so you will be building a trans tunnel as well. It was just easier to remove the floor forward of the seat riser and build the floor and front cab mounts from scratch. I just did a quick floor reinforcement of the floor where I thought the trans tunnel would end up and then built the tunnel after the drivetrain, body brake booster, and steering column were in position.

If you are keeping the Dakota fuel tank (I did), you will also have to cut a clearance notch in the driver side floor and the bottom 2"-3" of the cab back wall to clear the fuel tank. I removed a section from about the center of the cab to about even with the driver side frame rail, and probably 8"-10" forward of the back of the cab. The area removed also removes the original floor where the gas fill tube passed through it. Again, I thought it was easier to form my own cab mount and floor step then it would have been to adapt the original floor. The good news is on the passenger side, I only reinforced the floor around the cab mount with an 1/8" plate.
At a later time, I did end up removing all the seat riser because it interfered with the mini van bucket seats I used. Had I used a bench seat, the seat riser probably would have been useful to mount it.

Once the cab is in position, the motor and trans can be positioned. You will find the motor and trans will have to be moved back in the chassis about 5" or 6". This will require making (or modifying) the motor mounts and will also require moving the trans cross member back the same amount. It will require brackets to be added to the frame to support the trans cross member. I used the original Dakota motor mounts and modified how they were located on the frame, and I used the Dakota's original transmission mount and transmission cross member and modified the frame to accommodate the original trans cross member. I wanted to be able to buy motor and trans mounts on line if I needed them.

I'm running the Dakota power brake booster and its mounted on the firewall. That booster is pretty big, and firewall space is pretty limited, especially if you want to keep everything under a hood that closes. I made a cardboard template of the booster diameter with the brake pedal bracket attached, the positioned it on the firewall. It needs to be under the hood top (but as high as you can get it), it needs to clear the valve cover (and cover removal), it needs to clear the exhaust, and it needs to clear the closed hood side that gets closer to the motor as you move forward. There is very little room for error, it needs to be correct or something is not going to clear.

Moving the motor and trans towards the rear, then adding a cab that is 8" to 10" more narrow then the original Dakota cab, a brake booster and a steering column all present an issue with the steering column. You get to make brackets to hold the steering column and reinforce the firewall mounted brake booster that will end up attaching to the bottom of the dashboard. Then the column needs to fit around the brake pedal. Then you get to make a firewall mounting end. Once through the firewall, the steering shaft needs to clear the booster, the exhaust, the starter, the cross member, then turn down towards the steering rack. Some Double D shaft, a couple steering universal joints, and a steering column helm joint mount are very helpful. Cutting up a piece of wood 3/4" round dowel rod (with flattened ends to fit fully into the double D joints) makes that job a lot easier. But good joints and a good helm joint mount, not the cheap crap.

The radiator mounting is another project. Once you figure out where the grille is going to have to be mounted, you will probably end up cutting off the front frame rails at or about the front of the spring pockets. This is where your going to find out those Dakota frame rails and spring pockets are not centered with the cab, once you get passed the front suspension. Keeping the hood and grille shell straight, centered, and at the proper height, to the cab will be the highest priority. I bought a new Champion aluminium radiator for this truck. The radiator I got is for a 50-54 Chevy truck with a V8. The radiator fits inside the grille shell with side clearance, is a hood height, and has the hose outlets in the correct position. It also has an arched top that fits nicely in the Dodge (or Plymouth) truck grille. The only issue is that you also have to but a hose mounted cap and fill tube to go in the upper radiator hose, or you have to cut a hole in the top of the grille shell. I bought the radiator hose filler with a cap for around $20. The aluminium Chevy radiator was just over $200 + the $20 hose filler, you can but an aluminium radiator to fit the 39-47 Dodge/Plymouth grille for around $600. The Chevy one works great.
There are notches in the lower grill shell that the bumper brackets are suppose to pass through. I think they are a little low, even on the original truck. I'm not using that lower grill piece on my truck, so I get to put my bumper at any height I want, mine it 15" to the top of the bumper. I added 2" x 3" tubing from the spring pockets to where my bumper is centered and tacked them in place. I built my radiator support off these two 2" x 3" tubes.

The original grille shell had a heavy U channel that went under the radiator and attached to the frame. The fender support brackets were also attached to this U bracket, and the radiator was also bolted to this support. That channel on my truck was nearly rotted away. If yours is good, you can make bracket off your frame to mount that original radiator support to and your pretty much done. I had to build all this new, so early on, I removed the original stuff inside the grille housing and trashed it.
The original radiator support bolted to the grille shell with 3 (or 4) 3/8" bolts on each side. I bolted 1/8" x3" flat stock to each side using those bolts. It made those bracket long enough to be below the attaching point for the lower grille, then made a bracket (1/8" x 3" flat) to go under the radiator and welded both sides together. Then I added mounting brackets (one on each side) to attach my U shaped bracket to the frame with a rubber bushing between the frame bracket and the radiator grille support bracket. The radiator was attached to my U shaped bracket with ears to bolt to the mounting tabs on the radiator with 4 1/4" bolts.

When everything is in place, go back and finish the firewall, the floor pan. and the rans tunnel.

The last thing I can think of right now is the box mounting. The 39-47 box is 49" wide inside. That width is 4" wider then a Dakota box floor between the wheel wells. If you do not want to cut the 39-47 box sides, the Dakota rear axle is too narrow. I used a rear axle from a mid 70s full sized truck, and the 39-47 rear fenders will clear the tires and wheels unless you go to extremes. Gene

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