Hmmm...That leads me to believe that she's not immature, but merely frustrated with kids who are not her intellectual peers. I know this isn't what you want to hear, but it says to me that you might want to consider a grade skip.
Consider how a 7yo would act if she were cooped up with 4yos (or 5yos or whatever) all day, expected to play with them and do the same work they are doing. She might act out a bit, right? That's probably sort of how she feels in a regular classroom.
Have you read "A Nation Deceived?"
http://www.nationdeceived.org/It's free, and it's well-researched. You might want to take a look at it before you decide that a grade skip is wrong for her. It may be wrong for her, of course, but I think it's good to get the facts before you make that call.
(Full disclosure: we chose to homeschool rather than to grade skip our HG+ son. So I'm not a grade skip pusher. LOL!)
