My son's cello teacher (very generously) suggested JD when he was at a similar level to your daughter's when he auditioned (he's a cellist). I honestly didn't think he'd want to, then I didn't think he'd get in, and then I didn't think he'd stick it! But he did, and had five brilliant years there. The musical education is so valuable. We live in something of a musical desert, so it was great for him to mix with like-minded people. At home he'd always stood out as being better than everyone else, so it gave him a dose of realism to socialise and play with people who were often better than him. How old is your daughter? Our son was 13 when he started and I wouldn't have wanted him to go much younger, not because it would have been bad for him, but it's just such a commitment.
I wasn't so keen on not being able to choose his teachers, and the contact with teachers is much reduced, but the children are forced to be much more independent and take responsibility for themselves. It's a big financial commitment too, though we got a bursary that covered a portion of the fees, and we had to drive our son which meant five years of having no weeeknds in term time. It was a one and half hour drive, with lessons sometimes starting at 8.30. It was alright for our son - he just slept all the way there and all the way back! He carried on with some other musical things outside JD, but for him it was largely enough, so at least everything was done with on a Satuday and we weren't having to make lots of other trips out to things in the week. He is also our youngest, and when he started his older brothers had all left home, so we didn't have their needs to consider in quite the same way as if they had still been at home.
I don't regret our decision to let him go. It was definitely the right thing for him, though I wasn't always sure at the time. My husband and I got to quite like our Saturdays - he'd go walking, I went shopping! And we made some supportive friends among the other parents. Our son has just started his degree at a different conservatoire, and the musical education he had at juniors has given him a confidence he wouldn't have had if he'd just had lessons and played in an orchestra. He's got a much more rounded m usical education, and has had some great experiences along the way.