I sympathize with you! But I'd still say, don't skip your daughter, even though it means working to make her learning more interesting. Here are two experiences.
My husband's daughter had a Nov. 4 birthday. He and his wife (at that time) chose to start her early. From the stories he tells, it was a disaster for his daughter. She could do the school work, and she apparently made friends. BUT she had the behaviors, concentration span, and patience of a child a grade younger, and the teachers got very upset. Your daughter could feel "different" for her school career. (And then there's puberty, when her friends are maturing faster than she is. Ouch!)
Our daughter's birthday is Sept 22, and she's very bright, so we had the same choice with her. I talked to relatives and friends, some of whom had faced the same question, and they recommended NOT pushing children ahead.
One of the cousins (who could have been pushed ahead but wasn't), said "It comes down to: Do you want your child to be a leader or a follower? " He was always the tallest in his class, and one of the most coordinated. (Remember gym class, and picking sides?)
Anyway, we kept our daughter in the right class for her, and we are generally happy with the choice. She does extremely well in school, and her teachers love her. Yes, she is bored sometimes, even though she has two hours of gifted classes per week. I try to take her and her sister (also gifted) on trips, and to museums.
See what you can find out about gifted education in your area. Is it mandated? Are there other resources for you? Also, I've found that as the children progress, the work gets harder and comes faster, and the less they report being bored. (I've even considered taking them on family vacations in early Sept., since that is when they're most bored with review, review, review.)
Good luck with your choise. I know it's difficult. Feel free to contact me directly at ____@____.com.