Rabbits Moving Hutch

My doe recently gave birth and we've decided to upgrade the bunnies hutch Will they be worried if I move their hutch? I am quite worried because I want them to be happy in their new hutch

How recently is recently? How old are the babies?

How many babies? What accommodation are they currently in?

What kind of personality does mum have?

and welcome to the site

Yes, it really depends on the age of the babies. Definitely don't move them until they are out of the nest and hopping about the main hutch area. You'll need two hutches when they reach 8/9 weeks old, so my suggestion (unless it's really tiny) would be to wait until then and then move the boys or girls into the new hutch.