I've had most shipped to me. My DDB was the longest flight and I believe it was Continental Airlines, my daughter and I were an hour early at the airport we were so excited. The baked beans Golden retriever was on the same flight as they were waiting also. As soon as the crate came, I took him out and walked through the airport to the car. The dog was absolutely fine, sitting there like nothing at exactly his 8th week birthday.
That being said, I would worry much more about a grown dog with strength and a bunch of airline employees. We have been planning out multi stop flight for Nessa and we have decided to lock the cage and put signs in 3 languages Do not open. As they usually open to let the dogs out during changed flights which almost always turns into a news cycle with a tougher breed. The cage is going to be a mess but better that than having the dog shot on the tarmac.
Everyone I know that has exotic type breeds has the puppies shipped in with no problems. The only problem which is a bad one is if the plane gets delayed on the runway and its hot out, I remember a flight losing 26 military GSDs for that.