Are you running the original QBasic in an environment like DOSBox or FreeDOS. If that's that case, this might be a very tall order.

You could try something like QB64 instead which is something like 99% compatible with the original QuickBasic. Since that version is actually built using modern techniques, it might be possible to expose the Win32 API to it through a library or some other method and then you can use Windows Performance Counters for high precision timing.