I've been in the cargo bins of passenger aircraft for 19 years and have seen everything shipped--fish, chickens, bees, mice, snakes, penguins, bears, tiger and lion cubs, a leopard, pygmy goats, dogs, cats, turtles, parrots, military police dogs (DON'T try to pet them), iguanas--you name it, I've seen it--except I don't recall seeing rabbits. As rampers we try to make transitioning in and out of aircraft as stress free as possible for animals, but it's already a stress laden situation. The incredible noise tarmac side, in addition to the jostling of shipping, transitioning between freight house to van to aircraft side to aircraft bin, which many times we're loading the bags as we get the animals. Sometimes the animal has to wait before it can loaded into the bin where bags are going first. Sometimes we can stick it in an adjacent bin (animals are assigned their position in aircraft by the loadplanner) and buckle them in safely. Then the animal has to endure the reverse procedure at the airport of destination. I can see how it would overstress a rabbit.
To be fair, I have shipped my own dogs down below when I lived in TX, so I would recommend it as a way to transport. Most rampers try to make the trip as easy as possible for the animal. There are times if the flight is delayed and the weather isn't so great, we'll take the kennels into our own breakrooms and give them water if need be. Just yesterday I loaded several dogs on their way to San Fran.
So... just because I haven't seen one doesn't mean people don't ship them via aircraft--but I think most rabbit breeders know the limits of their animals. Plus it is very expensive; shipping isn't cheap and it requires a vet's certificate of examination to go on aircraft. If rabbits are shipped, then they'd be worth a lot of money, and I don't think they'd want to put a $200 rabbit in a situation where it could expire of fright and stress.
