Be certain that the information you give is correct - we all think we know everything about our children but as they get older it is possible that we dont - and if you inadvertently give incorrect info it might invalidate the policy. Personally, I would give her the responsibility of organising and paying for the policy to promote a bit of adult responsibility - you can always reimburse her for the cost privately.
My daughter has told her insurers that they can talk to me about her insurance and they have put this on their records - just incase of emergency.