If you want to change the teacher's mind, you can point out that introversion occurs in a higher percentage of gifted people than nongifted so the teacher really should be looking for the quieter kids if she wants to find gifted. We tried this and the answer was that "well quiet kids are not what we are looking for because they are not dominating the other kids. The purpose of GT is to take the dominating kids out of the classroom so the other kids get a chance to learn". This is a clear sign that our GT program is NOT for truly gifted.
Wow. That system seems really unlikely to find twice-exceptional students. Those kids, by federal law, HAVE to have access to the same educational benefits as their unaffected peers. They aren't limited to "good enough" educational opportunities... or "average" performance as a benchmark for whether they need help.
The worksheet approach also seems to be a barrier for children with emotional issues and difficulty with social settings. They are selecting for qualities associated with extroverted temperment, not gifted traits. In fact, it seems to me that the characteristics they are seeking are actually found MORE frequently in the "bright-not-gifted" group. I'd point that out-- and ASK to see the evidence upon which they are basing the (subjective) selection criteria. Because of course they wouldn't be using criteria that they pulled out of thin air, right? They must have EVIDENCE that such characteristics are uniquely associated with high cognitive ability... and that ability to gain educational benefit also correlates with those particular character traits. (Hint: it doesn't-- in fact, most studies support some degree of ability grouping, but also support enrichment for ALL ability groups.)
I'm sure that they wouldn't be
deliberately excluding THOSE
other kinds of children, would they? You know, the highly gifted, but shy ones... the ones with learning disabilities.

I'd offer portfolio items from home-- those which demonstrate what your DD does when she's not overwhelmed and dumbing down to fit in better.
I think that it sounds like you want to pursue it, given the early tracking and the consequences of that later on. Honestly, at 133, your DD
is the kid that most in-house GT programs can help the most-- she's obviously gifted, but will probably thrive with a slightly modified curriculum, similar-ability classmates and enrichment.
It's maddening that they don't see that.