A walker is one of the lightest, quickest items to move in the whole house, and the only real job is keeping the legs' height locks intact and the walker within reach the whole day.
Pro tip: If glide caps or tennis balls are worn, replace them before the move rather than after; a smooth glide matters more on new, possibly different flooring.
Watch out: Confirm every leg's height-adjustment button is fully locked before the walker is used again; a leg that slips down unexpectedly is a fall risk.