As a breeder I already picked my airline of choice. Before I picked I talked to all of them via customer service. I took time and asked questions then I decided. There is a new airline that caters exclusively to pets, there prices are the same as the airliners but the dogs ride right in the cab of the plane. I forget the name though, maybe someone on here knows. I would choose them but they only fly out of certain places right now. They told me they plan to expand in the future.
Do your research. Call tons of places. I wouldn't do it if I couldn't talk to the people directly.
Good Luck with your new baby.