Assuming it's the same as the older lil' Kawasaki (one 6V motor, small battery, one gearbox), you can replace it with any 550-class motor you want. I pulled the gear and pressed it onto the new motor (after knurling the shaft a little) and used red loctite. However, there is a lot of gearing reduction in that box and I was estimating that with the tiny tires it would need around 30,000 RPM to hit 4.5mph. Ours was running faster than that, which explains why the original motor wore out the brushes after ~6-7 months of running on a 14.4V drill battery
If you just put in the same 12V motor that is used on the larger power wheels and run it at 12V it won't be any faster than the original motor @ 6V, though it will have more torque (a recipe for disaster).
That said: a 12V rated motor in there should have lasted forever on 12V, unless it didn't have a fan. Was it a 12V-rated motor that you put in or was that a typo?
F-150 - 24-36V with homebrew 100A variable-speed motor controller, 4x 775 motors (no, it's NOT all-wheel-drive--look HERE
for more details!)
Pink Rocket Princess Mustang - 15mph, 36V, 4x 775 motors, homebrew PWM controller rev 2....
Hurricane - 24V w/50A step-down controller, 775 motors