Now that I think about it, Nicki and Annette, this is an interesting point. If Fanny was her mother's right hand gal, what does that say about Mrs. Norris' choice of her over the other children to come to Mansfield? Mrs. Norris originally proposes:

“What if they were among them to undertake the care of her eldest daughter, a girl now nine years old, of an age to require more attention than her poor mother could possibly give?"

Nicki's right about girls being important helpers to their mothers with the younger children. I don't think even Mrs. N would be mean enough to deliberately take away the one child who helped her mother most at home. However, I do think this is further evidence of her not being able to empathize or even to understand what is happening in anybody else's world. She has an idea and she runs with it, bossing and arranging other people's lives in the process without really considering what ill effects could occur. IMO, this is a very important flaw in her character.

This is further evidenced by Mrs. Price's thought:

Mrs. Price seemed rather surprised that a girl should be fixed on, when she had so many fine boys...

We know that in JA's own family, a boy was sent to live with childless relatives, was actually adopted, inherited an estate and ended up largely supporting JA, her sister and their mother. A similar thing happens in Emma, as well.

Of course, the Bertrams have an heir--and a spare--but wouldn't educating a boy ultimately do more for the family? He might become a minister, or go into the law or any number of things. But the best they can do for a girl is to marry her off, and given her lack of fortune, her prospects are not all that great.

I'm wondering if Mrs. N chose Fanny because--whether consciously or not--she wanted someone she could continue to boss around. A boy would be sent off to school after a certain age, but a girl would be home forever.