Of course it's doable. IMO, I think it's slightly overkill but this is your project. You'll need to manually determine the pin functions or search for a schematic of the cd player to determine the voltages. This link will give you a rough idea (it's slightly different) of how to proceed with this project (http://www.hardwaresecrets.com/article/71). This is to power the car cd player OUTSIDE the vehicle, do I have that right?
Because your car battery operates on 12V, it's probable the car cd player is the same. I imagine all car decks run on 12V, but I may be wrong; perhaps some decks are configured with a different voltage. If you could provide the model of the car cd player, I'm sure the forum can assist you better.