Hi! I don't know if this will help or not, but we had a similar situation. We've done both subject acceleration and a full-grade skip. There are pros and cons to each.
My DD8 has a September birthday and received early admittance to K, so she started K less than a week before her 5th birthday. Absolutely no problems there being the youngest since she was clearly at the top of the class academically and essentially the same age as most of her classmates, although there were a few that were a year or so older. She has always been a rule follower (able to sit still, raise her hand, do what she was told). 1st grade went well, too, but everything in class was easy for her. We started 2nd grade looking for a teacher who could differentiate, but we all ended up realizing she needed more than a 2nd grade teacher could give her. In November of 2nd grade she started going to 3rd grade in the mornings for reading, writing, math, art, and phy ed (because that was the best way for the schedule to work) and 2nd grade in the afternoon. The school was worried about her being so much younger that they didn't want to fully skip her. We figured she could handle it, but didn't push it since she had a ton of really good friends in 2nd, and this way she could have lunch and recess with them. But, she ended up making great friends in 3rd grade and really felt comfortable there as well. It ended up being a transition year. This year, with all of us in agreement, she is in 4th full time. It is going really really well. Sure, there is a boy in her class with the same birthday as hers and he is two years older than her, but truly you could look at the entire class and never know she was any different age-wise. She has great friends and is good with seeing her age-mate friends outside of school or even before and after school. School work is still easy for her, but a least she's learning new information and not sitting in a class full of kids learning things she already knows well.
In my DD8's case, the full-grade skip works really well, because all the subjects in elementary school are usually designed to be interactive (i.e., you do math when you're doing science, you practice writing when you're learning about social studies, etc.) Her 3rd grade teacher recommended that if she ever needs acceleration again that it be a full-grade skip for this very reason. Of course, this works in her case because the subject accelerations were for all of the core academic subjects, not just one of them. Also, while my DD didn't have any problems transitioning back and forth between the two grades, that could have been an issue. A full-grade acceleration, too, makes it a little less-obvious to the other kids. With a subject acceleration everyone sees your child coming and going from the classroom (although, honestly, young kids barely notice since lots of kids are pulled out for lots of things) and this can call attention to the fact that they are different. With a full-grade acceleration it's just not as obvious, although I'm sure eventually everyone will figure out the age difference.
My DS5.5 just skipped K and we did it now in part because we knew that this way he wouldn't eventually have to transition to a whole new group of friends. He has a November birthday, so there are kids who are already 7, but he's just a few months younger than most of the kids and, since he's very tall, you couldn't pick him out of the group either. He's a little bit more active than his sister was/is, but so are most boys in 1st grade. He still knows most of the academic stuff already, and he's had to learn some of the stuff that everyone else learned in K (the Pledge of Allegiance, where the bathroom is, etc.). He doesn't seem to have missed anything that a gifted kid can't pick up fairly quickly. Some other things we considered in his case were that he had a lot of friends who were in 1st grade so we knew he would fit in, and that he is generally even-tempered and easy going.
Which leads me to one other thing to consider, and this most certainly varies from school to school. In my kids' school there is a very wide range of ability and maturity given that there is also a huge socioeconomic range. We have a ton of ESL kids and a ton of middle class kids and a fair number of kids of highly educated parents. We have a fair number of kids who can't sit still for long even into 2nd grade and a fair number of kids who do exactly as they're told. But every school is different. So, before you make a decision, I would suggest you go into a few of the 1st grade classes into which you are considering moving your daughter and just watch for a while. See if you think your daughter is similar in maturity level. She if she would stick out socially or if she would blend in well enough. She what the routines of the class are. That alone could help a ton with your decision.
So, there are a lot of things to consider, as everyone else said, and only you know what's best for your child. Probably you already have a gut-feeling about it. And it is a big decision. But remember, that with these gifted kiddos, adjustments to their schooling always can -- and will probably have to -- be made and all you can do is do your best.
