Fred, 1st you mention a "little girl" and "she"...then you say "his"
owner?

I see no inconsistencies.

"little girl" and the first instance of "she" would refer to the child who
owns the toy.

"his" would refer back to the Furby itself, anthropomorphizing it in the
male gender. So yes, "his owner" meaning the Furby's owner, again meaning
the little girl.

The second instance of "she" would refer to the Mommy with the drawer of
batteries.