Your insurance policy which provides Liability coverage only would not cover any physical damage to your vehicle. For a fire to be a covered loss by your car insurance carrier you would need Comprehensive coverage on it. Your daughter's insurance would not cover this loss either for a couple of reasons.
First the SR22 policy that your daughter has provides only additional Liability coverage for her while driving any non-owned vehicle and also satisfies the state's financial responsibility requirements so once again only Liability insurance . Furthermore, since she was driving your car, your insurance policy would be primary and her insurance coverage would be secondary since insurance follows a car first and owner second. Even if she had Comprehensive coverage on her own car it typically does not extend to other cars that you have, only your Liability coverages extend to other cars you drive as excess or secondary coverage if the owner's policy limits are exceeded.
Without you having Comprehensive coverage on your car than the loss due to a fire would not be covered. If you did have Comprehensive coverage on it than it should have covered the loss, even if your daughter was the driver at the time of the incident.
We can provide you with an auto insurance quote for your new vehicle including physical damage coverage. Just put in your zip code and follow the pages. There will be no need to leave your home or office to purchase the insurance.