I would recommend that IF you plan extended stays in the rv that a class c is really not what you want. Had a guy I know buy a new 24 ft C kept it about 4 months was not happy with the size as they had to fold the bed to bring in rear slide, the dining area was small and the over all construction left a lot to be desired, paid around $70K for it and traded for a bigger class A (he has also gotten rid of it as they went back to a house). Overall they lived in the rv's for a little over a year.
We have a 28 ft which is big enough for 2 but no way with a large dog. Ours is on a E450 chassis and we do tow a 3000lb car. It handles it well, but not so sure on a 4500lb or so jeep. Yes we have 5K receiver but as others have posted it may not really be able to handle that weight in reality. Mainly they are lower weighted due to extensions on the rear frame, so that is something to think about.
I would recommend that you consider a small class A some are around 30-32 ft or
and would be better for you if you do plan extended stays. Most will still be with V10 or the new 7.3 or whatever it is. You will not have the concerns about the jeep either I dont think. You need to research a couple to see what their limits are. BTW the class A the guy bought had the v10 and got almost the same mpg as the 24 ft class c as well as what we get. Another thing to consider is how well the thing is insulated. Our c is not well insulated and it is a name brand, this is summer and cold weather I am referring to. If you will be in az we still get cold here particularly at night. day times temps may be nice but the cold is still here depending on where you are going to be. We are in tucson and it has been 80-90 day time and high 40-mid 50's at night. and its not winter yet.
So do the research, my BIL has a dp adventurer and he indicated that the lpg went fast when they stayed out in the thing again particularly in the evenings and night. I think most c's only have an 18 gal tank for propane??
Whatever you decide make sure to research well before you buy.