These were the very same reasons we didn't try to skip our DS7 and opted for homeschooling instead. (Though no one gave us the "they all even out by 3rd grade" speech, which is good because I'd have been rolling my eyes BIG TIME at that, as I really, really hope you were doing!!!)
Just be aware that you may want to force the issue a bit once she *is* in a school situation and you can see how she fits with those older kids. You may find you're changing your mind pretty doggone fast about that skip!
For our DS7, the choices were clear by 1st grade: grade skip--probably more than once in a couple of years--or homeschool. If your DD is not as prone to act on feelings of frustration, you may not see this as easily as we did. If you're the teacher, it's probably not a problem this year. But if you're not teaching her or in future years, be on the lookout. She may need more.
I hope whatever you decide is a great solution for your DD!