I agree with Challenger- you want the tires at the max air pressure while towing. Running them underinflated can lead to the tire overheating and failing. I would not go over the rated pressure cold though.

From the picture it looks like you need to lower the tongue of the trailer. You should have no problems towing a trailer like that with a 1500 provided it has adequate tongue weight. Get more weight on the tongue by moving stuff around in the trailer and/or go with a bigger drop on the ball mount/WD hitch.

I've towed enclosed trailers similar to that with my 05 1500 without a weight distributing hitch or airbags added to the truck with no issues at all.