Hi there
It's not usual for the young to emerge from the nest until about 2-3 weeks of age, so this is certainly very early, although it sounds as if your doe is trying to make sure they are warm if she's covered them in her fur.
The problem is, that because doe's are very territorial, especially after giving birth, if you try and place them back in the nest box, she may actual become aggressive and hurt/kill the kits.
My advice would be to leave them be for now- as the doe may decide to move them back into the nest box herself- if they stay warm, fed, and the area around the hutch is kept quiet, then they should be ok- it's better than risking interference at this early stage.
Regards Andrea
Veterinarian
bvm&s mrcvs 15 years as a companion animal veterinarian
That actually sounds very promising now- if she's used to a lot of attention from you anyway, that will really help, and you certainly couldn't have left the little ones uncovered, so your actions were correct. Hopefully they will stay in the nestbox for a week or so now, until they have some fur of their own!!
Andrea
Yes, you could keep them with the mum if they are females or neutered males- although sometimes mature females will fight, in which case spaying the females is beneficial.
You should be able to start handling them from about 2 weeks of age.