Airlines will be tracking pet injuries and deaths starting June 15th. Read the story here.
After June 15th you can check the stats on the DOT web site.

In the 80's I worked at Logan Airport in the Cargo Deptartment of a major airline for a short time, and witnessed first hand dogs getting loose, missing connections, death from heat exhaustion, and re-routed flights with the dogs whereabouts unknown. On several occasions I took dogs home because they had no where else to go after their flight was canceled at the last minute.

Upon arrival, most dog were stressed, exhausted and covered in vomit and diarrhea. It didn't take long before the breeders and frequent flyers knew that I was looking out for their pets and shipped their dogs only during my shift. On my shift the pets always had someone meet them at the plane and didn't board until the very last minute. We never left them unattended on the tarmac and always sent them home with clean airline blankets (unbeknownst to our employer) and water, and most got immediate potty breaks, even though we were under strict instructions never to take them out of their crate. We always took them in the office before taking them out (making a mess of the office by the way), but we always kept them safe.
My shippers were always grateful.
Not everyone is as conscious as we were. Use caution when shipping your dog and be sure to get the direct cargo phone numbers on either end and speak directly to the people looking out for you pet.

On a side note, we also shipped many animals for the Museum of Science and the New England Aquarium to include, dolphins, seals, skunks, snakes, sea turtles, alligators and fish. I was also responsible for shipping human remains, which is why I didn't work there very long!
Many airlines give pets frequent flyer miles, but did you know that funeral homes get frequent flyer miles to?