Has your daughter seen the film? I think if you wouldn't show your DD the film because of the language then I would think twice about the musical.
It is the most fantastic musical though and I can really understand why she is so keen to see it. Both of my DDs have seen it already and DD2 is about to see it again with the school . She is 14 and first saw it when she was 11 as a friend of ours was one of the ballet girls. DD1 also saw it at 11.
I would have been uncomfortable about them seeing it at 8 as there is a significant amount of bad language, but it really depends on how mature your child is and how you think she would cope with it. To be honest I have seen it three times now and each time I have been I would guess there were children younger than 9 there.
It's a tricky one..........