all you like. I have a ds who is also somewhat hypersensitive to sounds and who I had to watch last year in reception go from happy and enthusiastic to increasingly disillusioned with his peers and opting out. The school did try to give him more challenging work to get on with (and I saw what they were offering to him, it was stuff he would normally enjoy and find interesting and beetle away at at home for hours) and, unlike with your dd, did acknowledge he was unusually gifted. However, the work often went untouched and he made less and less effort with his peers. I am capable of acknowledging that I made his problems worse by asking him leading questions about what the problem was (eg once he'd mentioned once that the work was too easy, almost every day he got asked what he'd done or learnt at school, was it interesting or boring, why hadn't he done or said this or that in order to get something more interesting etc) and giving him the impression that I could move him away from the school at the drop of a hat if he didn't like it.
This year, I have gone out of my way not to adopt this questioning style, which only elicits the information you are expecting, rather than everything the child might have to say, and the school have been really good at working with him - as a whole person. There is, most definitely, nothing wrong with his social skills - he plays beautifully with older children, can be flexible, has a cheeky sense of humour - he just doesn't choose to use these skills much at school. Basically, he just has a problem with children his age unpredictably changing the rules of a game and has little tolerance of the idea that this may be because they didn't understand the rules in the first place (which are all rather obvious and easy to understand for him), rather than the fact that they are being deliberately very annoying. He has thus chosen to opt out, rather than get annoyed and have to put up with it. The school has been great at setting up playground games at break times which older children in the school help run so that children like my ds can enjoy and join in with their peers, and not have to be the one reminding everyone of the rules all the time. He is coming home happier as a result and, because happier emotionally and socially, much less condemning of the fact (ie less miserable) the work is generally too easy for him, and even offering up items of interest from the day for me to know about - prior to this, he was choosing to read on his own in the playground, or to play on the climbing equipment by himself and was basically doing a very good job of isolating himself, feeling isolated and then feeling generally not part of it. The school have also set up 1-1 sessions with him every week where he feels free to talk, explore his interests, do something a bit different and interesting and is made to feel that he is respected and his abilities are understood. This has also helped hugely. It's not so much about making sure he is being stretched in literacy and maths (which he probably still isn't) as letting him express his thought processes more freely and to feel free to express his feelings in a safe environment. The school is also aware that I think he just doesn't hugely like the noise and moving around that goes on in a KS1 classroom, but neither did my ds1. I don't think his dislike of that goes far enough to opt him out of it, but am aware that he and other children like him will be happier when they reach KS2 and there is a lot less of that (as his db was). Yes, he is a child that would have enjoyed a more "traditional" education, but his life is not being ruined by a more "modern" play-based one - not if I don't let him think that. He is, generally, quite a happy boy this year.
On another note, I have several relatives (and a dh) who were moved out of their school year to work with older children and/or were moved on full fee scholarships into private schools. All but one were then held back for a couple of years in scholarship classes at the end of primary or prep school so that they could be returned to classes with their peers. Mostly, the people this was done to were OK with the decision, although felt that they missed out in terms of sport and other non-academic subjects as a result and it obviously didn't prevent them feeling different and a little bit separate to be put in with older children - so mixed feelings on whether it was a good idea. As for the relative who was never returned to classes with his peers, who was generally a fairly introverted personality, he bitterly resents his mother for fussing and fussing, moving him to a new school and always banging on about his intellect. He ended up at university several years younger than his peers, miserable and bitter. He felt he was treated as a brain, not as a human being with social and emotional needs which should have outweighed his academic needs. I wouldn't want that to happen to any of my children.
Yes, it is difficult to get the balance right and you probably never will, but please don't let the school get away with thinking they can make you happy/shut you up by giving your dd free reading books and tricky maths homework, which is probably what you will get if you just tell them you have discovered she is gifted and that therefore they obviously aren't stretching her enough. And please don't let your dd think you feel her time is being wasted at school and she only does worthwhile stuff at home, because in my experience it is quite easy to pass that feeling on to your children without meaning to and make them unnecessarily negative and unhappy at school.