Tried searching, but wasn't able to come up with much.
http://www.koreaembassyusa.org/
Website for the Korean Embassy, though I couldn't find anything regarding pets. There is contact information, though.
http://www.seoulsearching.com/livinginseoul/pets.html
Seems to be a site for military personal being stationed in South Korea. The links don't seem to be working all that well, but there is some general information.