My suggestion is to let her stay with peers her own age, but push the school (really it will end up the teacher's responsibilitiy) to offer her enrichment type activities to keep her engaged in learning. It will also work if you offer her the extra enrichment type activities after school (drama, art classes, music classes...)
I was a young 4 year old when I started Kindergarten at a private school. Even then sometimes I was still way ahead of the rest of the kids and would be bored with some of the assignments. I felt the real difficulties of being ahead when I got to junior high and all the kids were ahead of me in the "growing up" part. I was the last to get to wear makeup, the last to get to date, the last to start driving, and all my friends (and boyfriends) were at least 2 years older than me. My daughters are very much ahead of their classmates academically, but I would not choose to skip them ahead a grade. Instead I work closely with their teachers to make sure their needs are being met for a more challenging coursework. My third grader has a beginning algebra work group, is challenging herself to be the top AR reader for her grade, has worked on an animal project and is peer tutor for a girl in her class. My first grader designed a class flag (took a survey, designed, sewed), is working on a class newsletter, wrote a book, and does extra jobs for the office. Once they get to Junior high there are much more options for advanced placement classes, and in high school they can take dual credit which will give them some college credit while in high school. All their extra work is fun, but challenging them to think critically, design and create things/projects and they have both really enjoyed doing the extra work. So, it may take some prodding by you, and you giving the teacher some suggestions for how to keep them engaged, and you seeking out extra opportunities for your daughter to use her intellectual abilities (extra classes, contests for art/poetry).