Not at this time. I'll go through my notes to see if I can find anything in the other Gilligans in the Dakotas. Have you checked the 1870 or 1880 census to see if you can find her on it with family? 1880 Soundex if she had younger siblings would be a good place to start. It lists the famlies of anyone with children 10 and under. Check you local LDS (Mormon Church) to see if they have the census you need, or the index books for the 1870.
Let me know what you find.