I flew with mine last year on American Airlines. He did fine, I just made sure that he had some chew toys in case his ears were popping. No one on the plane even realized he was there
I did call numerous times to make sure that he was still booked to be a carry on and I had heard that they only allow three pets per plane usually 1 in first class and 2 in other. It costed me $80 to bring him.
I did call several times about paper work I would need, rabies certificate etc... but the airline told me I wouldnt need anything?? and never asked for any?? I would find out and possibly take it anyway just in case so you dont run into problems.
We ran into a couple that has 2 chis at home that they usually take with them on the plane and they said that they had never paid for their chis to fly with them and that they always snuck them on???????? I keep wondering about the xray machine and how this could hurt them? No way I would take any chances