This is a great question, Penny. It's also one that only you can truly answer since each child matures and reaches motor-skill milestones at different times. A general rule of thumb is for parents to be involved with their children's brushing while they're very young to be sure it's done correctly, and to control how much toothpaste is used. There should be less than a pea-sized amount on your child's toothbrush, and she should spit out as much as possible. Some children want to do their own brushing, and this should be encouraged. If they are brushing by themselves, and if you and the dentist agree that they're doing a good job, congratulations. In the average child, this usually occurs at around 8 years of age.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.