There's nothing wrong with a 10yo running and training, even in a structured way.
1. Research severs disease. It will be your (her) biggest enemy. Never let her run on the road. Massage and stretch her calves several times a week.
2. Don't let her race further than 2km, maybe 2 miles occasionally.
3. She should learn how to run properly and do sprint training. No point letting her run wrongly from the start. Build up gradually.
4. If possible get her in a group with a knowledgable coach used to coaching kids that age. It's better in a group and they can become friends.
5. Obviously, she has to want to train. It's not like 5am swimming training when it's ok to drag them out of bed. A little bit of gentle pushing is ok once she's into it - parents have to push kids a bit or they'd never do anything.
Good luck with it. My kid statrted training at 10, fortunately in a good group with a good coach with good attitude. 5 years later and he's still going, and still building.