Can a Doppler shift of 3Hz be detected in a frequency of 1.2 GHz?
It all depends on your frequency standard. 3Hz in 1.2GHz is not possible for cheap 10MHz standards, TCXOs even, but with a decent DOCXO or rubidium standard, it will be straightforward. The trick is not to try to count the frequency offset, but to compare your received phase with a reference. For a 3Hz difference, the comparison will spin a whole 3 times round in one second.

From 100Hz, it will be rather easier!