A kids bike is simple to move once you deal with its two odd problems: a chain that stains everything it touches and tires that can overinflate in a hot truck. Handle those two things and the rest is just a bike.
Pro tip: A short piece of foam pipe insulation, split and slid over the top tube, is a cheap and reusable way to protect bike frames on every future move.
Watch out: Do not fully inflate tires before a move in hot weather; heat inside a closed truck can build enough pressure to blow a tire.