The accuracy of time measurements depends on how accurate you get the beam. So if you cover (red line) the IR LED and the IR receiver like on the picture you'll get best results:
The NRF24L01 communication is very fast, if the first message is recognized it's about 1ms, the second (if the first fails) follows in 2ms, third in 4ms and so on.
The IR signal is also very fast, much less than every "standard" IR signal (remote controller use about 16-32bit!) because of it's slim code.
Two cars parallel. This also depends on the construction, see the picture for optimal results:
So the real trick is to use more than one IR LED'S in a row within a special angle.