A floor-standing drill press is a heavy cast base, a tall column, and a head that slides up and down, and that head is exactly what tries to slide or tip if you do not lock it first. Securing the quill and separating the head from the column keeps the move manageable.
Pro tip: Take a quick photo of how the belt is routed through the pulley steps before disassembly, since re-threading it from memory at the new shop wastes time.
Watch out: Never carry a floor-standing drill press assembled and upright through a doorway or down stairs; the tall, top-heavy column tips far more easily than its base width suggests.