It depends on how your Dad feels about exposing himself to the liability of a young driver. If you do something and you're sued, your father could end up on the hook. My wife and I have a LOT to lose- house, investments, etc. No way did we want that exposure. So, my daughter's car is registered and insured in HER NAME alone. But, many (most?) insurance companies will extended any household discounts to you, even though it's an independent policy. (Things like multi-car, etc)
We saved quite a bit by doing that - we pay the same for a much more robust policy as she could have bought a bare-bones one on her own for. With lawsuits getting larger judgements all the time, don't skip on liability coverage. Some friends of ours