How to drive power MOSFET at 1 MHz
I have done the 'roll-your own' MOSFET driver and it works well enough for frequencies below ~16kHz, but to drive at 1MHz, you will need a MOSFET driver for sure.  Fast switching times will be critical and the roll-your-own method will not be adequate.

The recommendations that I'm giving are typically used for a half-bridge setup (DC-DC converters, motor drives, etc.), but should lead you down the right paths.

I have used the FAN7842MX successfully for frequencies up to 60kHz on TO-220 packages (lots of capacitance to overcome).  It only has about 300mA of instantaneous gate drive current.

The IR2011 series would probably be better.  It has 1A gate drive current capability.

I can't remember the part number, but there are some with higher ability to drive the circuit.  At 1MHz, you need a solid gate drive.