Some air lines will let you carry animals in the cabin with you, Delta being one. If you book early enough they should let you take the bun in the cabin with you in a small carrier if he would fit under the seat in front of you. You would need to have him checked by a vet and a health certificate issued within the last 7 days, usually. Also an airline approved carrier. Call and ask around if any are free, how much it would cost etc. I would not put him in an airline that uses cargo because they tend to leave animals out with the luggage readying to be loaded (in whatever weather) – though you can find some airlines that will not do that and leave them in A/C until they load and have temperature regulated cargo spaces. Be CAREFUL though because often the person at the front desk has no clue about animal procedure.
There is also the option of driving, rather than flying, though for such a long drive a flight is probably less stressful for all involved.
Plenty of people move and bring their animals with them!
House rabbit society’s travel information page:
http://www.rabbit.org/faq/sections/travel.html
House rabbit society’s experience moving with animals:
http://www.rabbit.org/journal/2-10/rabbits-on-the-road.html