I started kindergarten when I was just barely 5 years old and they wanted me to go in at age 6...thing is I was testing academically above whatever the kindergarten standards were so in I went.
Fast forward a year, they wanted to hold me back because of immaturity and social problems. (yes I flunked kindergarten). But I could read, add, and do other skills above the level of the other students so my parents opted to let me go on.
I never did well socially in school but was always above average academically. So I think there is a trade off there. You just have to weigh in whether the risk is worth the reward...also you could keep her in the regular grade for her age and provide after school tutoring for added academic advancement.
But who knows, I might have been socially inept at any age so it's really hard to say.