Fast switching with RTL inverter
Perhaps a gate driver IC is appropriate (certainly lower parts-count) as @JohnD has suggested. Most drivers provide charging currents well over an amp for both rising and falling edges provide large dV/dt, and some have low quiescent current draw.

That said, you might improve the rise time of your circuit with a supplementary PNP pull-up transistor that is active for a very short time, pulling the NPN collector up with a short, fast, large pulse of current. This allows you to use a larger pull-up resistor (R1=10k).
Note that the PNP Q4 starts to draw about 10ma current after a time (about 0.5 us). This static current may not be wanted for a low power driver, especially if the PWM input pulse from logic source V3 has low duty-cycle...(much less a problem at high duty cycle).
A diode D3 might be a safe idea so that ramping up V1 to its +20V doesn't fry the logic driver with a killing pulse through C2.
Note that a faster switch Q1 is used rather than 2n2222.
R3 is chosen with care to set the static current of Q4 to something around 10ma. Since this current is very dependent on Q4's \$ H_{fe} \$ this quicky design is a bit too simple. When parts-count climbs, that monolithic IC driver becomes more attractive.