After several incidents, UA has become my "don't even think about them" airline. All airlines have some issues occasionally... but putting a puppy in an overhead baggage lock? The "per 10,000" is a more accurate way to look at it as obviously they carry the most pets. One would think more experience would lead to more expertise... but no.
El Al managed to drop Cara's crate 2 times and Moose's once. We were beyond livid and distressed over it. However, no one else had issues so I chalk it down to bad luck. Still, If I fly a pet with them again, I'm going to raise heck up front about the last time and video them loading and unloading.
The Australian laws stipulate that the animal has to be able to stand and turnaround without touching the container. They will not allow two to travel together, and you have to get a certificate signed by a vet that they are fit to make the journey within a day. There are a number of things to consider about flying, and when I shipped to USA they were put in the cargo and not let out for 16 hours during the flight - just as well. When I shipped to Hawaii, no rabies there, he held onto everything, and as soon as he was out of his crate at the other end, he had a gigantic piddle. And smiled.