hi....good for you for thinking of your dear little ones well being, a move can sometimes be a huge trauma to them.
I am hoping bkitty and piparskeggar will reply b/c they have both recently gone thru moves with their pet family and all went successfully for them.
one think I will suggest is maybe using a light product that works really well for stressful events such as a trip to the Vet, car ride, moves too....its usually avail at most Vet clinics and some good pet shops....just make sure you get the one for Pets and NOT the one for people, the Pet one is alcohol FREE...it will say on the bottle.
heres a link to it thru iherb where I order many of my products from.....good luck on the move and keep us posted:)
Has Kitty and Puppy been introduced to each other? If not you may want to introduce them to the smells of each other. Like taking a towel or something with Kitty's smell over to Puppy's house and vice versa.