First of all congratulations on the move! How exciting you are starting a new chapter in your life
Your animals will have to cope.
I would work on familiarizing smells. You can start that now. Bring some smells from the garden house into your room. When you move, I would move some familiar things first. You could do simple things like leave some tissues in the garden house, and then bring them back to your hammies for bedding. Leave some rattie toys over there and then bring them back. You get the idea.
For moving day recruit lots of help and friends with trucks and see how much you can do at once. It will be stressful so just accept that!
Best of luck!