I would move the baby and eggs to the nesting box with some bedding in it. The mom will probably hear the baby's calls and go to it. I am no expert though...

I would not stress too much about a new baby... budgies have been doing this for ages! They know what they've got to do.

Proud owner of
1 dog
3 budgies : OLIVE . WILLOW . STORM
1 rat
many fish