I remember my teacher at Canadian Tourism Collage told us the pet can get a heart attack when they travel by air.
When you check in your pet, your pet goes to the cargo area. In the dark, all the sudden they will hear loud engine noise and it scares them. So it is not good for them to travel on the plane. However people sometimes need to take them on the plane and the airlines try to make the pets as comfortable as possible by temperature-controlled and pressurized cargo (Not all the aircrafts have one. So you need to call and book your flight. ) or ship without owner.
I just saw this Delta airlines’s news.
Pets No Longer Accepted as Checked Baggage or Cargo on Boeing 767 Aircraft Effective June 10, 2012
(June 8, 2012) – To ensure the best possible experience for customers traveling with pets, Delta is amending its policy for acceptance of live animals traveling on Boeing 767 aircraft . Delta is proactively attempting to contact affected customers to assist with making alternate travel arrangements. Customers with questions may contact Delta Reservations at 800-241-4141 (International) or 800-221-1212 (Domestic).
You can also find information from these links;