Will your insurance cover damages if your daughter is driving your car and there's an accident and the other person is at fault?

Yes but with subject to Your daughter is not excluded from your policy, you do not have a "limited" policy, your daughter holds a driving licence and has not consumed any alchohol and the insurance policy is not void.

The damages to your car and to the third party property of the person can be covered up to the limit specified in your policy.