Peak detector (peak event)
I don't especially like the idea of doing this with a differentiator, because your gaussian pulse has a relatively flat top, so there will be a time when the derivative is nearly zero, so that the moment when you detect the peak will be fairly noise sensitive. 

If the shape and amplitude of the input pulse is the same each time, you may be able to get what you want with a standard op-amp peak-detector followed by a comparator:



What this is doing is not trying to detect the peak event directly, but detecting when the input (IN) falls by one diode drop below the peak. When this happens, you'll get a rising edge at OUT. 

After each cycle, your micro should assert the CLR line to clear out the peak detector.

You could reduce the delay from the peak to the output edge by using a schottky diode at D2. If your pulse is very slow, the value of C1 and R1 also need to be chosen large enough so that the capacitor doesn't bleed down too quickly after the peak.

The diode and FET types are just the default ones in CircuitLab. You'll want to choose these more carefully.

You'll want to choose an op-amp appropriate for the time scale of your signal, and you'll also need one that is okay being used as a comparator (e.g. one that doesn't go crazy when its two inputs are not at the same voltage and that can recover reasonably quickly from being driven to the rails).

Edit: I updated the schematic, adding R2 in the FET drain, to avoid extreme currents through D1 in the event the pulse arrives while you are resetting. Ideally you'll give your reset pulse at a time when you know the pulse won't occur. Otherwise, you'll need to make R2 big enough that you don't blow out OA2 or D1 if it does arrive when CLR is asserted; and make the CLR pulse width long enough to fully discharge C1 through R2.