It is relatively easy to measure picosecond intervals - look for "time to digital" converters.
Before you spend too much time implementing it, you will have to consider how to distinguish photons from your light source from any other photons that happen to hit the detector. Be very very careful with safety: 5mW (depending on wavelength and other things) is the maximium amount considered safe from a laser. Yes, you can easily get 400mW and 1W diodes, but they are definitely not safe.
If you use a powerful laser (i.e. >5mW) then you should protect those around you by looking directly at it the first time you swiitch in on - it will blind you and thereby stop your experiments before they damage innocent bystanders!