Designing an op-amp circuit to generate a digital pulse from LDR
I think one of the main disadvantages of your circuit is that the Vin+ is connected to ground aka negative supply rail and this will be pulling your output into significant saturation because Vin- is several volts difference from it. I'm also concerned a bit that as the device isn't rail to rail you might get some oddball situations where the output inverts because the common-mode range on the inputs is exceeded.
I'm thinking along the lines of what is called as a data slicer. This circuit will tend to keep Vin+ and Vin- closer to each other. Here's a half idea of a circuit which I'll make a few points about underneath: -

Assuming the light input to the LDR is constant, the voltages on Vin+ and Vin- will, apart from noise be very close. In effect the output will be a noise amplifier but in the presense of a small data signal, the output will amplify and reproduce the data as CMOS level signals - this is its main use.
Because you are not using data and you also don't want a big noisy output, you can put a resistor across the capacitor so that the input to Vin+ is slightly less than Vin-. Maybe try 1Mohm. This will seperate the inputs sufficiently to stop noise breaking through and also give you a control value to optimize the response you need. I'd try a 1Mohm pot (in series with 100k) across the cap and do some testing.
The output will be a decent pulse because the op-amp is being used as a comparator. NB I know this device works quite well like this.