I have moved a lot with mine.
The first thing I do is bring USED bedding of theirs... I never wash their stuff before the move... this way the same scent is on their stuff.
Second, when I get to the new place I set them up FIRST. Everything of theirs get taken out and put into a place so they feel comfortable.
Also, during the move, I keep them crated, this way with movers or people in and out there is no chance of them getting loose.
I also only give them access to one room at a time in the new place so that they slowly get acclimated to the new location.
If possible I try not to leave them alone for the first few days at the new place... it usually works because I am busy unpacking anyway.
Good Luck... mine always do just fine!