The refractory dome and flue on a pizza oven are built to hold extreme heat, not side impacts, so the real risk in a move is a crack from being knocked or dropped, not the weight itself on portable units. Confirm it is cold and pad the dome like glass.
Pro tip: If your oven has a masonry or ceramic fiber dome, avoid the impulse to load it flat on its back; keep it in the orientation it was built for to avoid stressing the refractory seams.
Watch out: Never move an oven that has been fired within the last 24 hours; residual heat in refractory material stays dangerously high long after the flames go out.