Last time I made a pulse generator to drive, among other things, some mosfets. When loaded with a gate its rise time increases to about 200ns, trying out some capacitors I get the same result with 5nF. While it is not quite right to approximate the gate with a simple capacitor it helps to ballpark the driver needs.

The output swings 10 volts on 200ns (10%-90% of 12.5 volts) on a 5nF cap. I = C*dV/dt , so 250mA are flowing. If I want a faster driver I’ll need to add another stage, as the BC548 won’t give me much more current. LTSpice kind of agrees with these numbers, but I need to put 15nF to match the rise time (and the current increases accordingly).