not having any kids myself, I'll just have to guess on this one.
I recently helped a friend move who had kids, and to keep them occupied - we gave them each a box. We told them "you can take whatever you can fit in this box". Took them all day to pick and choose what they wanted. They didn't know they were getting a 2nd box...LOL
If I had a child (who was too young to really help), I'd probaby send them off to Grandma's or the sitter's on moving day - or maybe a neighbor who has a kid around that age...Maybe even have someone come over to just entertain the child so I could direct the moving process.
Have them sort socks, silverware, tupperware, or something equally safe (no knives, of course). Although it's going to be of little benefit to you, the child will feel useful.
Hope this gives you some ideas, and good luck!