Eddie Murphy has a few family-oriented comedies that feature children of color... Daddy Day Care, Dr. Doolittle, Haunted Mansion.

I almost hesitate to mention these, becaue they're terrible, but my DD likes them, so yours might. Disney is doing a pretty good job of mixing races on their TV shows, and two that feature positive black girls in particular are Jesse (that girl is right about your DDs age) and Ant Farm (which also happens to be about gifted kids).