Building laser doppler vibrometer for measuring frequency of 1 MHz
Maybe consider the principle that atomic force microscopes use.
They reflect the beam (very weak diode laser) off a vibrating object (in that case: the AFM cantilever) onto a quadrant photodetector.
After that you can condition the 1 MHz analog signal using standard electronics and ADC.
You don't necessarily need a quadrant photodiode, a differential one would also work. Or even a single one to some extent. The main advantage is cost, as you don't need an optical table and precision mounts. You also don't need to preserve phase of light as you do for interferometry. Therefore, you also don't need coherent light. So a well collimated LED will do.