Looking at the specific snippet of dialogue, it's not so much too intelligent as much as too antiquated.
It's a fantasy world, which is quite different then our world. So here, the antiquated maybe going to be accepted.
Having one character say "Mother, when can we expect dinner to arrive?" and another character say "Hey Mom, when's dinner?" is going be inconsistent and unsettling for readers.
I watch for this all over the novel. I never change the tone in this world in this matter.
But if everyone in the novel (overgeneralizing here, but you know what I mean) uses "Mother" or everyone uses "Ma" or everyone uses "Mom", then that more or less ties all dialogue together and allows the reader to notice important differences (such as a precocious seven year-old).
Yep. That's a constant trait all over in this world.
Here are two another examples. Here the seven years old girl is already an adult woman. Regardless few things are changing drastically in her character, she is still speaking on this way, even in her adult age.
"Mother. Please hear me out."
“Your mother knows that you’re right.”
"No. Mother is wise and she is always right.”
And I would probably keep her at age seven. Nine seems too old. This is purely my opinion though, and I don't really have any significant reasons to back it up!
Yesterday I played with this a little and she will remain seven, because of few reasons. She would be too old is one of them, just as you mentioned.