I ship dogs all the time. I use Delta, Alaska air, and American Air lines. they will ship APBT
's but I have my vet ship them as different breeds to keep people from asking any questions. They dogs have to be at least 8 weeks and must have a health cert from a vet. I have clients ship dogs for me to train and then I ship them back. I also breed so i will ship dogs in and out all the time and have never had an issue. You do have to be careful in hot/cold weather but if the temp is dangerous they airline will tell you. they look at weather.com before the dog's flight is booked. I also give the dogs a dose of benadryl just to have a sleepy flight. I do not believe in tranqs at all! I make sure the dog does not eat dinner or breakfast or have water in the am before the flight. I use shredded news paper or a blanket for the bottom. You also have to have those plastic water bowls to clip on the side and a zip lock bag of food so they can tape it on top. They do that encase the dog's flight gets delayed like overnight. That way they can feed and water the dog but they will not take them out of the kennel.
Don't let any of that worry you the problems you can have are limited. I hope that helps you out.
As far as someone had posted earlier about a ground shipper, I personally would ship air over ground. I have shipped dogs as little as 150 with American airlines to 300 with delta, that is one way of course. oh and Continental will not ship APBT
's but if your vet will fudge the health cert you can ship as another breed. I use lab, viszla, dogo, any of those types. Stay away from calling it a terrier mix because that means pitbull! I would only use continental in bad weather because they have climate controlled hubs (at the airport) and the area the dogs is kept is climate controlled too. They are more expensive so i use other airlines first.