Here's an interesting article on a new airline that specializes in transporting pets.
http://www.msnbc.msn.com/id/31083094/
There are a lot of problems involved with transporting an animal via plane, and this system appears to have solved a lot of them. For example, they have a vet tech on board to monitor the animals.
It's not the best time to start a business, but this might be the exception that proves the rule.