The March, 2006 Airline Pet Travel Report contains pet incidents for the month of January, 2006.
January 2006 is fairly quiet, but unfortunately Delta reported one death and Continental one Injury.
The death was a 2 year old pug named "Porkchop" who was found motionless upon arrival in Atlanta. The owner chose to take the dog home and no autopsy was performed. It's difficult to draw any conclusions without further information.
The injury reported by Continental was an Australian Shepherd named "Rosie" who escaped from her kennel during the flight and received a small cut on her nose. She was not used to being in a kennel and was able to chew her way out of her kennel during the flight. This is another incident that might have been avoided if the dog was more acclimatized to her kennel.