http://qatar.usembassy.gov/passport_faq.html

Q. We are Americans living in Qatar. We just adopted a Vietnamese girl and she is living with us there. How do we get her an American passport?

The same process mentioned above can be used for children adopted overseas by American citizens. While adoption by a U.S. citizen parent does not automatically confer citizenship, it does qualify a child for expeditious naturalization, or citizenship upon entry to the U.S.

Check out the link above...