Many air conditioners won't run properly unless connected to a 30 AMP supply. The fan will run, but the compressor will not.
If you want the best, buy a Honda or Yamaha rated for a 30 AMP output...about 3000 watts. After you recover from sticker shock, there are other options. About $2300. It weights a mere 90 pounds. If you go to the gym regularly, you might be able to load it in your pickup bed...or not. You might need another person to help. It will run about 3 1/2 hours while running your AC before you have to refuel.
Two Honda "2000" watt (1600 watt continuous) generators can be paired in tandem to supply the 3000 watts and run your AC. That's about $2200 dollars of so. Obviously starting, running, connecting, fueling, servicing two engines is the price you pay for less weight. And two will be noisier than one 3K.
If the sticker shock still has you shaking your head, many here have used Champion brand generators with good success. Two Champion 2K generators can be paired just like the Hondas, and they cost about $600 each rather than $1000.
I have a single Generac 2200 watt, 2000 watt continuous (undoubtedly inflated numbers) I bought for $600. I've used it for 4 years, and I love it. But I don't attempt to run the AC. I draw 15 AMP power out of it to run the microwave and a couple other things. It CANNOT be paired.
Tip for any generator. Set it up at home. Plug in your home microwave and try to run it. If the generator won't run a big, home microwave, return it and get another. The inverter/generator part of the machine may have problems. The microwave test is a true test as long as you have a full-bore, high power home microwave. The startup demands are the critical part of the test. Startup will really tax a 2K generator, but one that works properly will do the job.
I've used my Generac as backup power during outages. It takes planning, but I can run the fridge or freezer, TV, lights, my computers, and so on. Something like the fridge should be run more or less by itself until it shuts off after achieving temp.
It won't run my 240 volt well pump or hot water heater, but it will keep us going otherwise.
DO NOT buy a cheap "construction" or "backup power" generator. You can get one that delivers about 7000 watts continuous from Harbor Freight. It's a WONDERFUL generator to run your house, but they are VERY noisy, and your fellow campers will put sand in the gas tank before they put up with that racket.
The reason the inverter generators are so expensive is that they are RELATIVELY quiet and they deliver clean power. But quiet is relative. Most campgrounds require you to shut down during quiet hours, so if you're thinking you can run the AC all night, think again. If you're boondocking, your neighbors will still object...and don't forget that the noise your generator makes will do a great job of masking their assault on your gas tank.
Good luck. I camp in the Rocky Mountains, and I don't need AC (though I have one). But I understand your need if you are in a hot, humid climate.
One last note. A PUP has NO insulation. Your furnace works overtime in cold weather and the AC works overtime in hot weather. It will be cooler inside the camper, for sure, but don't expect miracles. 13,000 BTU is no match for 100 degrees and 80% RH when you're trying to cool what amounts to a 1000 cubic foot canvas bag.
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