I moved to and back from Hawaii with a rabbit. They put her in with the luggage. LOTS of rules - and none of the airline employees agree on them...
Weather dependent, and a major hassle, but at the time, it was doable (just). The return trip two years later was VERY hard on the bunny. Not recommending it.
If you are that committed to an animal, maybe charter a small plane with a bush piolet? You would have a better idea of the pricing than I would.