While your daughter is still part of your household you should be able to keep her on your car insurance policy. Once she moves out on her own though normally she would indeed need to get her own auto insurance policy on the vehicle, and thus it would help if you signed the car over to her or at least added her to the title so that she has insurable interest in the car to get insurance on it.

If she moves out your insurance company will not typically allow you to continue to cover her and the vehicle since they are now located at a different address than your policy address. When she moves out her "official" address should be that of where she is living currently and garaging the car, not her previous address of your (her parent's) house. Even if your address is what is on her driver's license once she moves your state likely requires that she updates her address and thus her new address should become her new "official" address with the state, insurance carrier, etc.

If you try to keep her insurance with you and do not inform the insurance provider that she has moved out than they may be able to deny claims since there was misrepresentation on your part about where she was living and where the car was being garaged.

If you help her get her own policy once she moves out of the house than you would need to speak to your insurance agent to see if there is any reason to continue her on your current car insurance policy as well. Normally there would not be a reason to do so if she has her own policy on her and the car she is driving.

Liability laws differ by state so a lawyer that specializes in this type of law in your state could give you the best response about liability and the responsibility that each you and your daughter would have financially if she was in an accident in the vehicle that is in your name and under your insurance policy.

We can tell you that in general both her as a driver and you as the car's owner can be held responsible and thus could be sought after financially for the damages she may cause to others if at-fault in an accident. As the owner of the car you have vicarious liability for those that operate the vehicle, meaning your daughter or anyone else that drives the vehicle with permission

A child getting insurance on their own does normally cost more than if he or she lives at home and stays on the parent's insurance policy however once a child moves out of the house they typically must obtain their own insurance policy since a parent's policy will not usually extend to a child that has moved out of the parent's household. Your daughter can start to shop around for affordable car insurance here with us.