Hi, I've worked on several Arduino projects including a quadrotor, and I think I can help you out on this one.
One of the projects I worked on involved reading a signal from the source of a laser, and after a delay (in microseconds), I had to send out a second signal to trigger a "Pockel Cell", something that amplified the laser.
While this is not exactly the same, it is roughly in the same time frame, and I am aware of the problems associated with having such a small time frame, and we can work it out.
I just need to clarify one thing: will the timing from the LEDs be done initially, or will it have to be dynamic. Also, most LDRs have a response time in milliseconds, in which case, it is possible that the LED blink will not be detected at all. I trust that your sensors and circuit have a fast enough response time.