I suggest putting your cats in a crate (possibly a dog crate if you have one) with a small litter box inside. If the trip to your new house is a short drive, putting them in a regular size cat carrier will be enough. If your move is anything like all mine, its very busy. When you get to your new home, place your cats together in one of the rooms in your house with a litter box until you get settled in. Stick a “do not enter” sign on the door so none of the movers open it and let your cats out. Your cats wont know the new area and if your kitties get outside, they'll be lost and might run away trying to get to their old home. Good luck with your move! 
