I converted my 51 Plymouth to 12v - ground. Not real hard to do. Had to rewire it anyway because the PO's mechanic did a real hack job putting in a new aftermarket and universal (fits nothing) wiring harness in it. He kept it 6v + ground, but used a 12v harness, so all the wires, including the battery cables, were undersized. Lol
You will have to change all the bulbs there are 12v equivalents for them all. The starter doesn't care. My electric wipers needed reducing to keep them from beating themselves to death, lol. I had to use a 12V starter solenoid, added a 12v coil and a ballast resistor. Heater blower motor was replaced with a 12v one.
Probably a few other things but my 51 doesn't have a lot of OE electrical stuff.
Here's what I did for an alternator
http://www.yourolddad.com/12-volt-conversion
Some of the wiring issues
http://www.yourolddad.com/rewire-it
Blower motor change
http://www.yourolddad.com/blower-motor
None of those links are comprehensive, just stuff I ran into. If you have questions, ask away.
Why I converted? Because I could, lol. No seriously, I wanted good headlights, nothing 6v, including LED ones, qualify, imo. I am running GE Nighthawk 12V, 7" round, LED headlights. Those are good. I also want a thumping stereo, yet to do. I also want AC, no 6v option I know of there.