My vote is NO, don't do it. I've passed on all 3 of my children skipping a grade' b/c they were smart enough to do more...Here's why:
1. They will graduate and leave home a whole year earlier and attend college a whole year earlier with all peers older then them.
2. They will not be able to date their older peers - my rule.
3. They will not be able to get part time jobs with all their new older peers b/c they will be just one year too young.
4. They will not be learning to drive and getting their driver's license in the same grade as their new older peers.
5. By keeping them in their current grades they have experienced and will continue to experience wonderful successes and enjoy being at the top of the class. This is not a bad place to be and there are wonderful life-long benefits to that kind of self esteem and position.
6. They still have to grow emotionally, and that can never be rushed. Intellectual growth comes in spurts. There will be times when their effort and abilities will be taxed enough. Don't stress them out.
Let them be normal kids. They have to learn to get along with all people eventually, or so we hope. It is nice that she is processing homework and schooling easily now in 2nd/3rd grade, she has years of education ahead of her, where it won't be so easy.
Have her commit to something else, like music / piano lessons to challenge and motivate her. Remind her that she is blessed to have this ability and opportunity and that it is ultimately her responsibility to continue to try hard.