Customs in any country can be a pain to deal with. Rabbits usually aren't covered by any rules, so a customs official might not know what to do when one comes through. They aren't that common, so not something that would be seen every day (where a cat or dog could be on every flight possibably).
Try to ere on the side of caution. Get a health certificate. Get any import rules printed off so you have them, try to include websites so there is some way to look it up if needed. If you think you might need a passport, then look into getting one and even actually getting one.
Also make sure you have him booked on the flight well in advance and that they take rabbits. He might not be able to be in the cabin with you. The carrier needs to be suitable for air travel, and some airlines have different requirements for in the cabin and in cargo. If you are using a few different airlines, they could all be different, so you need a carrier that can work for all of them.