You can check with your insurance company’s agent to make certain, but usually your daughter’s injuries that resulted from the accident with the motorist that did not have insurance would be covered under your uninsured motorist bodily injury (UM) policy if she is part of your insurance policy.
UM typically covers you, the insured members of your household and your passengers for bodily/personal injuries, damages or death caused by an at-fault uninsured or hit-and-run driver. If you are involved in an accident where the other driver is at fault but has no insurance, your policy will cover your medical expenses, up to the limit on your policy.
Likely you and your daughter will have to prove that the medical bills and doctor bills are related to the accident. To find out for certain if your daughter's injuries will be covered by your insurance contact your insurance agent and go over the terms of your policy.