The little girl spent her days helping out Sarah-1 with the laundry.
She didn't have a name.
Was she a member of the family? She didn't know.
She wasn't in any other scenes - that she did know.
What was her purpose?
To do the laundry.
So that's what she did.
There really is a little girl in the first scene of the Carousel of Progress. She isn't named or given a speaking role. She is helping Sarah, the mother, with the laundry. It isn't the daughter, Patricia, either - she's in her room. It's just weird.