sensitive. they can live in a familiar environment. as it is hard to live in a new environment for human, more than it is difficult for pets.
as they are speechless but they have feelings. and the owners can easily feel it.
yes, the first and main thing is making sure that your pet is good in health. if you have any doubt, you must bring it to a veterinarian. and ask him if it is good to move to a new house.
if the veterinarian is agreed and say that your pet (dog or cat) does not have any diseases. you can process your moving, otherwise, you have to wait until it 