OpenIntro,
We used Continental Airlines when we shipped our dog to UK. They have a contact agent here, PBS. We asked PBS to pick up the dog at the airport and deliver it to us at our front door. Everything went smoothly, thank GOD! We're going to use them again to ship our dog back to US.
The Rabies Vaccine should be still valid (1 year time line), and all vaccinations should be up to date and the health cert should be within 1 week of travel.
Good luck..