Inverted Pulse Generator
Here's a fairly direct solution.


The significant realisation is that this is a one-shot (monostable) oscillator, which is edge-triggered. To detect an edge, a series capacitor is the simplest method.

So the solution starts with a series capacitor. Next we want a 1ms delay. We already have a capacitor, so a resistive load will give us the delay we want. The signal then drives a transistor so we can drive the output.

OUT1 is the signal we want, but it suffers from a slow rise time. The OUT2 transistor sharpens it up for us, but is now inverted. So finally, OUT3 inverts again and gives us the sharp, 1ms, inverted pulse we want.

Drawbacks of this approach are the reliance on the rise time and source impedance of the input signal. You'd need to know more about the situation to know whether these are issues or what to do about them.