A loaded wine rack is deceptively heavy and the bottles are the real risk, not the rack itself. Empty it completely, box the bottles properly, and the rack becomes a light, simple piece to move.
Pro tip: Reserve your priciest bottles for a smaller, personally carried box rather than trusting them to the truck at all.
Watch out: Never lift a full wine rack by its frame; the combined weight of a dozen or more bottles can snap wood joints or bend wire supports.