I agree that kindergarten is about a lot more than the curriculum. It's about classroom expectations, getting into routines, learning to interact with your peers. And it's a REALLY sweet time, a gentle introduction to school that has plenty of playtime and fun. There are lots of extra resources for gifted kids - try looking into some of those. They can be a lot more fun and creative, whereas pushing into the next grade can (at worst) just be higher expectations and more work at a younger age - where's the fun in that?
And it's also a LOT easier for teachers to vary the curriculum a little to keep the interest of children that are a little ahead of the curve than to vary the classroom to take into account the social and emotional issues of a younger child.
And if she's always the youngest in her class, that can be an issue as well. Maybe not quite as much if she's a very tall child, but if she's younger and smaller than the other kids, it can be difficult.
If she stays in kindergarten, she'll probably be one of the most capable kids in the class, which will really help her get along socially, give her a shot of self-confidence and set her up for success. If she transfers into first grade, she may be able to keep up, but she probably won't be at the top of the class. Then there is the social aspects - older kids may play rougher or may socially exclude her. At some time or another, almost everyone has had to deal with some kind of childhood cruelties, aggression, or playground trauma, and by pushing ahead one grade, she'll be exposed to this earlier. Same thing for "dating", video games, movies, cell phones and going off to college.
Fast forward 12 years. Do you *really* want her moving out of the house and into those college dorms and into the "whole college scene" a year earlier? Even very smart kids can have poor judgement and one extra year in the late teens can really make a difference in their confidence, their "sense of self," their wisdom and ability to make good decisions.
I'd recommend at LEAST giving kindergarten a shot. It really is a sweet time with much less pressure to sit still, write neatly, sign your name, "stay one green!" (ugh), take responsibility, do your homework, etc.
If you're wrong, you can advance later on (2nd or 3rd grade) with no stigma. But if you advance now and later wish you hadn't, there's a LOT more stigma with being held back later.