I don't know, either

Rosemary was sitting in the living room eating her breakfast the other morning and Batman (think it was Batman - could have been some other cartoon) was on the on the TV. The following impressed us:

Chris: Why does the red-headed girl call the other red-headed girl 'Red'? Why doesn't anyone call her 'Red'?
Tasha: I don't know.
Rosemary: I don't know, either.

We were impressed both that she was listening to our conversation and also with the correct use of the word 'either'. I wonder how long we will be marvelling at her linguistic development? Presumably we'll stop at some point.