A musical jewelry box has two things a plain one does not: a wind-up mechanism with small gears that can strip under a jolt, and a lid mechanism that can trigger the music if bumped in a box full of other items. Both need to be locked down before it travels.
Pro tip: If you know how to access the movement, a drop of clock oil on the mechanism before long-term storage keeps gears from seizing, though this is optional for a simple move.
Watch out: A fully wound musical movement is more likely to strip an internal gear if jostled hard during transport than one left unwound.