She's your child, your choice. If you wanted her to see it you could watch it at home with her before the school sees it with her, or you could just say no.
We had this in about Year 5 with dd and the first world war film about the horse, 'War Horse' it was a 12 and dd was 9 (dd also loves animals, a lot!).
I watched the trailer and was in tears, dd was unmoved.
I sent the school a letter which said something like ... "In general I am not in favour of children watching films which are a higher certification than their age; I do feel it sets an unhelpful president."
I told the school I had watched the trailer, I was moved to tears (at the senseless loss of life in war) yet my nine-year-old was pretty much unmoved, in fact she commented that it was 100 years ago, as if this meant the loss of life was less relevant (as they would now be dead anyway!) I explained people had died young, unable to get married and have families or fulfil their lives. DD does have autistic tendencies so she may well struggler more than the average child to understand this.
I felt for the teachers to try and explain some of these very tough emotions to children is a very big ask and I am not sure that films are a very good way to do it.
So I told the teacher I thought one of their challenges would be in conveying the enormity of loss of life for those involved in the First World War, and said if they genuinely felt that War Horse would assist in doing that, then I would give my consent for my dd to see the film.
I said this on condition that there was a space made available for children who chose to stop watching the film part way through.
Many years ago I have walked out of the cinema on at least two occasions when watching films that I found distressing, as an adult. So if dd did become distressed watching War Horse then I would rather she could leave the room.
I also said to please give families enough warning if they went ahead with this so that we could watch the film at home with our child before it was shown in school.
Just some ideas which may apply to you.
It was so little of a deal in the end I can't remember if it was shown or not!