Just for information. I went back to the store yesterday with my daughter to get measured up again and she was borderline 1/2 size larger, so the original shoes were probably the correct size.
@landlord, apart from correct sizing and keeping toe nails clipped I'd suggest your daughter try a different approach to tieing her laces to prevent her foot slipping forward in the shoe when running downhill or during rapid deceleration (which may be a contributing factor?).
Here's a . I started using the one on the left a few years ago and can recommend it.
If this is the only pair of trainers it's happened with then it does sound like a quality issue, but as someone who frequently wears shoes out in the toes in my case I'm definitely at fault! For some reason for which I've never had a medical opinion I walk with my big toe pointed up and it has nothing to do with the size of the shoe. To be honest I think it's just bad habit as I wiggle my toes like mad when I'm sitting at work / on the bus etc and rub them against the top of the shoe. It's rare I have a pair of socks that doesn't have holes in the toes within a few weeks!