
Every time I've moved house (being a Forces child, we moved a lot!) we simply cleared one room, shut the animals in there till the removal men had gone, then loaded us all into the car and set off too. At the other end the animals (dogs, cats, guinea-pigs) stayed in the car till we sorted out a room to put them in there, and repeated the exercise. Never had any problems.
You could always invest in a couple of crates for them to keep them secure while people are going in and out of the house all the time.
:)