You don't want to use old transistors. IRFxxx have been around practically since the beginning. They have very high capacitance, especially drain-gate (which gives rise to Miller effect).
The 5V drive is also insufficient for a regular type part. IRL540 should be used, which is logic level. But it still won't be much faster, because the lower threshold means more charge has to be delivered over a smaller voltage range; and with the same series resistance available, even with a strong driver, you're limited in speed. To get much greater speed from a given device, you have to goose the drive, with a higher voltage (say +12/-5V), or even with high voltage pulses (20 or 30V peak, decaying back to regular gate drive voltages, at a similar rate as the Rg*Cg time constant itself).
Modern devices have about 1/3 the total equivalent capacitance, rated gate resistance, and better Rds(on), so they are much better to design for.
As for the load: what are you doing, and why is 1MHz+ important? You should analyze that ringing better. There are excellent ways to deal with it, which aren't too hard to work with. This deals with not only the ringing, but filters the high frequencies away from the load (not too important with LEDs, but important with loads like motors and Peltier devices), and most importantly, filters them away from radiating into space and disrupting communications from AM radio to air traffic control!
Tim