Although there is such a thing as a cruise ferry, they are not equipped for the rough conditions and long distances of transoceanic voyages. I do not think Cunard is set up to accept your car as checked baggage, though it might be possible to arrange freighter travel with your car, if you are flexible enough.
You can ship your car separately, of course. You can use containerized shipping, where the car is packed in a shipping container and loaded onto a freighter, or arrange for RORO (roll-on-roll-off) shipping, where it would be driven onto and off of the ship— but you would not drive it on and off yourself. You would drive it to the port in Europe, then pick it up from the port once it arrives in the U.S. As such, you would need to research which companies operate out of which ports— a freighter leaving from Rotterdam and arriving in Los Angeles/Long Beach won't do much for your holiday from Naples to Montreal.
There seems to be enough of a market that the cost is reasonable, under 2000 USD or so between Europe to North America, each way, when you consider not only the freight cost but loading and unloading fees, port taxes, document processing (Bill of Lading, etc.), and so on. (By comparison, it costs around $1500 to ship a car by car carrier from coast to coast within the US, maybe less now that fuel prices are low). But that does not mean it is easy, as there are various legal requirements and restrictions.
U.S. Customs and Border Protection has a guide on Temporarily importing a vehicle, car or engine into the U.S. which links to other government sites for obtaining customs bonds and getting NHTSA safety certification. Transport Canada similarly provides an overview of entering Canada with foreign-owned vehicles and a related FAQ.
As it is complicated, you can also hire a professional service to handle the logistics; try a search on freight forwarders or forwarding agents in your area.