Our Purrscilla camps with us.
One of her favorite spots is in the storage cabinets above our bed.
When we're not using it ourselves (the bathtub, that is), we keep the litter box in the bathtub. It's out of the way and gives kitty some privacy. The tub also acts as a "litter box within a litter box" by containing any litter that gets tracked/kicked out.
Tidy Cat clumping litter is used. Pees go in the trash. Poos go down the toilet. I've had some replies from folks expressing concern as to possible damage/problems to the plumbing system caused by the kitty litter. Our kitty has been camping with us since 2009 and I have not seen any issues. Besides, the only litter actually going down the toilet is what has attached itself to the stool, and I consider it minute. When I inspect the inside of my black tank after rinsing, I see nothing but the black bottom of the tank.
Like ours, your first cat camping outing will be a learning experience. One thing we learned was that our cat needed places where it could have an unobstructed view out a window. Our trailer has venetain blinds on all the windows so we had to raise them and just use the curtains for privacy. This way, the cat can just go underneath the curtains and see its outside world.
Another thing we discovered is that pet loops in campgrounds bother our cat because the sites are predominately occupied by campers with dogs. Our cat is actually more relaxed when we disobey the rules and camp in a non-pet loop because there are NO dogs. When camping in pet loops, Purrscilla growls and hides when people with (especially lively) dogs pass by. You don't have this activity in a non-pet loop. I'll take my chances with the park ranger/management. So far, no one has ever challenged me on it. To me, camping with a cat isn't much different than camping with a hamster, turtle or goldfish.