Depends what you mean by Long haul!! Do you mean all the way to New Zealand?
Rabbits can't fly in the cabin, even on domestic US flights (I work for a US airline). We transport pets in the hold on a daily basis and the majority of them arrive the other end fine.
So that's why some Americans get stroppy with me when I explain that the buns have to go in the hold because of the risk posed to wires if they escape. The airline I work for allows cats,dogs and household birds in the cabin only (and chihuahas are the common pet at the mo.... bloomin' noisy yappy things :lolSome do as long as you've got an approved pet carrier...you can carry pets in much the same way as hand luggage...ask on any American rabbit forum
One consideration would be that it would be without hay for the duration of going to the US as you're not allowed to put hay or straw in the kennel.