I need to transport my FDM 3D Printer because I am moving.
What are the precautions that one should take?
Should I dismount the motors and axes?
I would definitively unplug the electronics as far as reasonable and fix the motors to the frame so they don't slide during transport.
Should I have a housing to avoid dust and other mechanical issues?
Yes, fix the motors and any other loose/movable parts. Remove the bowden tube if it's there, and any other parts that are sticking out. Put the whole thing in a a bag to protect from dust, and put the bag in a box to protect it from getting beat up. Remember to calibrate it when you're ready to set it up again.