I have two bright kiddos. While I have communicated to the school about each of them, I have ABSOLUTELY felt the need to advocate even more so for my DC whose personality is more like your DC's.
DS5 is quiet, but gets along well with his peers. He BLENDS and is compliant. I worry about a teacher not having any CLUE about what he already knows and how quickly he learns, so (so far) I communicate for him. This works well so far with the right teacher. I prefer to communicate objective measures, but this can be challenging when your DC is young and has not taken many tests or assessments. Communicating what books your DD is reading, or the types of math they enjoy could be one way to communicate where your DD is at in her learning.
My other DC is quite extroverted and outspoken. She doesn't try to blend and it is harder to "miss" her because of her personality. I guess she's a "squeaky wheel."
"Bright children" do not all have the same personalities - I am living with two examples of that.
