The K-1 status indicates your fiancee is a fiancée of a U.S. citizen. As such, the foreign fiancee may be eligible for a Social Security number and for employment. To apply for a Social Security number:
•     Complete an Application For A Social Security Card (Form SS-5); and
•     Show documents proving the following: Immigration status; Work eligibility;  Age; and Identity.

•     Take your application and original documents to your local Social Security office. If you live in the New York City metropolitan area, Las Vegas, Nev., Orlando, Fla., Phoenix, Ariz., or Sacramento, Calif., you may need to apply in person at your local Social Security Card Center.

All documents must be either originals or copies certified by the issuing agency. 

[1] www.myfianceevisa.com offers additional useful information relevant to fiancee visas.