I have traveled across the USA with rabbits (flying and driving) and I think you could do it. When I fly, I take my rabbit as a carry-on in a flexible airline approved pet carrier and put him under the seat in front of me. I keep a harness on him (it makes the attendants happier) and stroke his nose and keep an eye on his eating/drinking. The people in security always love seeing a rabbit and they actually say it isn’t as uncommon as people may think.
Also, there are a couple medications that can help. For my 17+ hr drive, my vet gave me a medication that helps digestion under stress and a very mild sedative and Barnaby was as happy as could be the next day (he has a sensitive GI system). I also keep critical care with me and I have used a syringe if he wasn’t eating even his favorite snacks. If they aren’t drinking, you can try watered down juice to entice them as well.
Make sure you call the airline ahead of time and get them to specifically approve, otherwise the people checking you in can be hesitant. If the airline gives any trouble, I compare my bunny to a cat, which many airlines allow. I would let them know that people are less likely to be allergic to rabbits and the rabbits are a lot quieter. You definitely should avoid putting them in the cargo area like some people do with their dogs and cats, since rabbits can be sensitive to the loud noises and pressure changes when landing and taking off. I have heard of people sedating their rabbits, but that seems like too long for that.
I also agree with Azerane, try to acclimate your rabbit ahead of time and find a vet just in case!