I agree to keep her in the cage for at least 24 hours after moving to help her feel settled. Perhaps keep the cage half covered with a blanket for extra security. If she's going to be inside, I would also put the cage in an out of the way place while moving all the furniture in (such as the laundry or bathroom) so that there's not so much movement and noise going on around her.
I finally moved out of my parents house last year and took my bunny who was 9yo at the time. He doesn't take well to change and it took him 2 months to come out of his hide box. He'd only come out to eat/drink and would be really skittish and go right back in. He stopped using his litter box for a long time too. I kept his cage exactly the same and my new house was calm and quiet. It just took him a long time to go back to normal.
I'd say keep him in his cage for the first little while and keep his cage the same. Let him come out if he wants to explore but don't force him. Expect that he might loose his litter box habits for a bit until he gets used to the new place. Also move the rabbit last so he's not around with all the commotion of moving day.
Keep her in the cage when you move and let her get settled in. When she is relaxed and acting normal start letting her out to explore on her own terms. I'd probably keep her on flooring thats easy to clean for the first little bit and keep expanding the area as she does good with her litter box habits/chewing.