Moving a laundry pair means combining two different jobs. The washer needs draining and drum-locking shipping bolts, while the dryer needs its vent and possibly a gas line handled. Do them as a sequence and label everything.
Pro tip: Do the washer and dryer one at a time and label every part bag, since the hoses and bolts are easy to mix up.
Watch out: The washer must be drained and its shipping bolts installed, then removed before use. Both steps matter.