Normally insurance coverage follows the vehicle being driven even if it is borrowed by another driver that has their own policy. In a situation where you are hit by an uninsured driver and the vehicle you were driving is also uninsured, it may be possible to file a damage claim with your insurance provider since your policy would normally apply on a secondary basis.
Your friend is ultimately liable for the damage that he caused to your vehicle. It is possible that your insurance company will cover the repair, assuming you have comprehensive and collision coverage on your policy, but they will go after your friend to recover what they paid for the claim.
You could always claim the accident as if you were driving but I highly recommend that you avoid lying to your insurance company. If you file a claim, they are going to want to know what happened so there won't be any way to avoid involving your friend other than being dishonest.
Ultimately, the decision to file a claim or not will be up to you and your dad. You can use our State of Insurance report to give yourself an idea how much an At Fault accident will affect your rates, but there is no way to tell with 100% accuracy until you are charged for the accident by your company.
Insurance follows the vehicle and pays primary after an accident so the claim would need to be filed with the company that insures the car. If that policy does not provide enough coverage for all of the damage then the driver borrowing the vehicle would have to use their coverage for any additional damage.
The rule of thumb is that the insurance coverage on the vehicle you are driving is primary in the event of an accident. Since you will be borrowing a vehicle, your car insurance would provide secondary coverage in the event that you are involved in an accident.