I think that the school should have notified you. I think a bit of forewarning though, might have given you the chance to prepare her a bit better.
I do think by year 9 a child really should have a bit of background knowledge already about WWII and the holocaust, and it wouldn't really be appropriate to stil shield them from that. It is a moving film, I'd help her focus on the positives that came out of Schindler's actions. I wonder if she actually saw the end sequence, if they only showed snippets?
it might be worth getting the whole film and watching it with her so she can discuss it without you. It is a big thing to deal with.
ds1 is going to be watching the diary of Anne Frank soon, he is year 6, so 11 but also asd and so socially immature. He is prepared for it though, having visited her house, concentration camps, and the holocaust exhibition in the Imperial War museum. I don't think anything can be as hard hitting as seeing the size of those dormitories in Neuengamme. However, the school did let us know, and give us the option to opt out, and it is only a PG!
dd is 12 and watched Sarah's key with us a couple of weeks ago. It's a 12, and I would really recommend it for older children. Not so violent as schindler's List, but a very moving film.