Airplane engine on R/C Car?!?!
I'm 100% sure there are motors that will put out at least 1500 watts... Take a look at the Hacker motors, for example the B 50 L series.
The gearbox you should use depends on the motor. There are high and low revving electric motors. A high revving motor should be geared down to something like 1:6.
Sanyo RC2400 cells can take 40 amps easily. Even 60 shouldn't be a problem, at least, if you're not drawing that much current for like 3 minutes continuesly. Take a look on the web what the electric pylon fliers put their cells through...