If that Peg Perego Gator is anything like all the other Power Wheels type stuff, don't expect too much. My kids had a Power Wheels Chevy Z71 pickup truck a few years back- which I converted to run on DeWalt 18 volt cordless drill batteries. It had the two forward speeds and reverse. The "gearboxes"- one at each wheel, were simply a reduction unit. The two speeds and reverse were accomplished electrically. A resistor was employed to drop the voltage for low speed forward, and a simple polarity-reversing switch built into the "shift" mechanism allowed reverse.
I think the gator might be a little different. The only reason I can think that is because in the lower speed it doesnt have posi trac, but in the higher speed it does. Or it might be the other way around I cant remember. If you come across one it couldnt hurt to tear it apart and have a look.
On the flip side maybe that would suffice for a transmission of sorts, you could over volt the motor for more power up hill, and cut it back on the downhills and flats to save some juice.