While my wife and I have been long time campers (5th wheel) about a year ago we purchased a Lance truck camper for some long distance travel. Our first trip was from Iowa out to Portland, OR and then up to the Canadian Rockies. Were were gone a few days short of 3 weeks and drove a little over 5000 miles and the only time we removed the truck camper was to drive the "Going To The Sun" road in Glacier. So long as you level the camper properly you can use it off of the truck.
Our Lance has a built in Onan 2500 watt LPG generator and I also packed a Honda EU2000 in a front mounted storage box. I don't think we ran either one at all. If you were to run an LP powered generator a lot I think it would use a fair amount of fuel. I purchased the Honda because I felt it would be a lot handier refilling a gas can vs a propane tank. Also, a lot of campgrounds have restrictions on hours of use for generators. If you want to run the AC a lot for your pets, I think you would be better off finding campsites with at least electrical hookups.