Will your insurance company still pay for the damages to your car if your daughter who has no drivers license and who was not at fault for the accident drives the car at time of accident?

Probably not, as most policies only cover drivers not listed on the policy if they were given permission to drive. If you gave your unlicensed daughter permission to drive, then you can be issued a ticket. However, if the accident was not your daughter's fault, then the At Fault party is responsible for the damage they caused to your vehicle, regardless if the other party was licensed or not.