Toughts...
Travel Trailer: Definitely don't travel with your animals in the trailer. Even the most substantial trailers are bouncy nightmares for animals. Sensitive animals like birds, bunnies, and turtles won't survive this daily punishment.
RV Rental: The cost will be prohibitive. A friend of mine rented a small Class C to relocate to Orlando and between the mileage and the five days rental it cost her over $3k. I can't imagine what it would cost if you took your time and enjoyed yourself, but it would probably be cheaper to buy something.
A van with a small travel trailer sounds like the safest option for your pets and the most affordable option for you. "Car camping" out of the van would be even cheaper, but not as safe for you.
