There isn't a build in timer with 1ms resolution.
One thing you can try is to use a PWM output to drive a HSC input and then you can count the number of HSC counts from the time you start measuring until the time you stop (e.g. receive a response). The differential count will give you an idea of the time it takes. A 2KHz PWM with 50% duty cycle driving HSC gives you 0.5ms resolution.