You can send a certified copy of the judgment in your lawsuit to the folks who issue birth certificates in IA and that should change your name on your daughter's birth certificate.
Ask them what form you need:
Iowa Department of Public Health
Bureau of Vital Statistics
Lucas State Office Building, 1st Floor
Des Moines, IA 50319
(515) 281-4944 recording
http://www.idph.state.ia.us/eh/health_statistics.asp