Yongsan Pet Care Center

I actually found this information on the Osan web page.

PET INFORMATION
Cats and dogs may be shipped and are subject to customs and quarantine regulations.

Osan Veterinary Treatment Facility (VTF) provides full service veterinary medical care for dogs and cats, however, use of the VTF is a privilege as other mission requirements may take precedence. For additional information call the Osan VTF at DSN 315-784-6614 or commercial 011-82-31-661-6614.

Health and rabies certificates are required and there are specific time restrictions. Pets must be vaccinated against rabies at least 30 days, but no more than 1 year prior to entry. The health certificate can be no older than 10 days from the date of travel. If you do not meet these requirements there is a 10-day mandatory quarantine period. If quarantine is required the pets will be taken to the National Quarantine Center at Incheon International Airport.

The Pet Care Center at Yongsan US Army Garrison can pick up your pets and board them at the Pet Care Center for a fee based on size and number. Reservations and a power of attorney are required. For additional information call the Pet Care Center at DSN 736-6426 or commercial 011-82-31-661-6426.

Pets should be shipped directly to Korea without any layover in Japan or Hawaii in order to preclude possible delays due to Japanese or Hawaiian quarantine requirements. The military flights chartered by AMC have restrictions for shipping pets. Contact your local transportation office for more details.