OP, your daughter has years and years to make a claim, if it is the case that there was clear negligence (although, honestly, it doesn't sound likely), and the only thing she should do is make sure that you have a copy of any relevant documents that flow from the accident.
I would definitely hesitate to claim against a school in this situation. Whilst I don't add my voice to those yelling 'down with compensation culture' (I think there should be accountability in many cases) I think there is a real risk that teachers just stop taking kids out on trips if claims are made in this kind of case.
I know you've said you won't sue, but that may be in response to this replies on this thread. People always say 'you should sue 'em' without knowing anything about the facts, so with the best will in the world, ignore them. Suing someone won't get her better faster.
This is your little girl, you're tired and worried, but kids do brilliantly at getting over things at that age. DD1 had two similar fractures before she was 6, and she's as right as rain now.
Your little girl going back to school in the most low key, non-dramatic way possible would probably be the best thing, and I'm sure she'll feel lots better soon.