A lady adopted a kitten from me in 2003, and needed to move to Lebanon last fall. Air France and (I think) KLM were very friendly. The best bet is to call the carrier and negotiate what you want to do. They often handle international animal transports on a case-by-case basis.

You will need to check the destination country's rules on vaccination, bill of health, and quarantine policies. I think that this can be done through the American embassy.

Good luck!