I doubt that you'd have major issues with the FET turning on substantially faster thahn the bipolar unless Q1 was a seriously low Ft part. If the LED current gets even say 20% above nominal then Vbe will be seriously high compared to normal (if 0.7V usually then = 0.84 V at 120%) and at +50% current Vbe = 1V+ and the transistor is trying very very hard indeed.
1 kHz is OK for many things but depending on duty cycle you MAY get effects that some people can see and if you are moving the LED, and depending on what it is illuminating, you may get motion artefacts. eg if you move the LED at 1m/s then in 1 mS it move 1mm so you have the lighting effects of 1 PWM cycle spread over 1mm. Fairly fine - you may see surface patternin. At 5m/s and 5mm/frame you can probably see the PWM patterns as dark / light sequences on an illuminated surface.
A base capacitor is probably a bad idea. If time constant is of the order of a PWM frame period or longer you start to get mean DC at the gate and the FET may run in partially on semi linear mode. A bit smaller Tc you round the pWM corners and slow the transitions and add heat to the FET. Exact effects depend on how hard Q2 is driven. Turning a transistor on across a charged capacitor tends to create undefined results and high current peaks unless specifically designed.