The size of the tank is not as important as the size of the motor. I'm going to assume this is probably a small compressor. It will probably be a little difficult to do a full job but I could see a panel-by-panel job being feasible.
The purple cheapo harborfreight HVLP gun uses 6 cfm. I could see you being able to paint a panel at a time with your compressor running constantly. Grab an in-line dryer filter thing (they are little red orbs) and go for it. You'll have to experiment with the paint thinning and get to know the hvlp a little. The guns really are very light and since you really don't need to paint more than a panel at a time and you can mix up paint on the fly more-or-less because it doesn't need a hardener, I think you would be fine shooting the paint. The sanding however is hard work... I'm not sure if you'll be able to do that. I'm pretty young and sanding is definitely hard on your neck/back/arms.
I would recommend getting a piece of scrap to practice on with the hvlp before shooting a car.

71Ford:
Nice Job! Lookin good in red! I hope you're ready to cut and buff though.
To tell you the truth, I just buffed parts of my car and the gloss improved ALOT and it was pretty easy. Used 3m buffing compound on my cheap HF rotary with the wool bonnet on the foam pad. Took the gloss from semi-gloss (almost flat black, ew) to glossy. I didn't even wetsand (even though I should have.) If you wanna knock out that peel, I would start with 1000 grit then follow up with 1500 then 2000 then some good hard buffing!