Welcome aboard the RoadTrip America Forums!
Before wandering off into the daydreaming of places you "just HAVE to go", go back and read the first set of responses you got. You have to deal with the realities of what you're proposing. Even if it's possible, it is going to be very expensive. RV rentals are not cheap, and using them is not a way to save money. Typically, even four people traveling together can get by on less by renting a decent sized sedan and staying in lower-cost motels. Remember that RVs get, maybe, ten miles to the gallon, so the trip you've laid out, at roughly 8,000 miles is going to cost over $3000 just in gas, plus the rental, plus fees for camping sites (no - you can't just pull over by the side of the road), plus the biggie: the underage driver fee. I assume from your "post-Uni gap" comment that you are all under 25. In that case, for every one of you who will do any driving at all during the trip there will be a $25/day extra fee for the entire length of the trip, or $2500 per driver Since I can't see you getting any base RV rate of less than $750/week, that means you'll have a minimum of $15,000 in expenses before you even park the RV for one night or buy one mouthful of food. If that doesn't phase you, then you'll have to find a company that will rent to 'underage drivers' in the first place and make sure that you have all your insurance coverage in order before you rent (or you're rental will get very, very expensive.) Only then will you be in a position to plan an adventure of a lifetime.
Sorry to be such a cold, wet blanket - but those are the hard, cold facts.
AZBuck