Some time ago I read about laser sensor which used ICs that designed for handheld radios. And those radio usually below 1GHz frequency, something around 400MHz. I think diode must handle frequency a little higher than that. You can google laser sensor teardown pics. Not sure if it related to your question, but maybe it will help. What would be Doppler shift for 3km/h? I think the same formula may be used as for radars. Also from my understanding some laser sensors only measure distance, and then estimate speed based on continuous distance readings. Because long time ago I have seen PCB of laser sensor which contained pretty old FPGA connected to diode through some simple ICs, I think just amplification and some conditioning. I doubt there may be anything higher than 100MHz, pretty old design. But I may be wrong. Did not researched this topic for a long time. Main problem with lasers is good optics, lenses. At last time I've checked this laser related topic