If you are going to pursue an IEP anyway, I would suggest that you ask the school to evaluate her more comprehensively. You can cite both the existing anxiety and the significant difference between verbal and nonverbal on the KBIT.
Again, the KBIT is a screening instrument, so you can't put too much weight on the results, but I will mention that her test profile is very consistent with what you are reporting about her academic strengths and interests. The expectation for a student with strong verbal and average nonverbal would be that she would excel in language-related areas, like reading, writing, and history, and be average to high average in mathematics.
The social issues, anxiety, misperceptions, and hypersensitivity are also not unusual in kids with this kind of cognitive profile. Variously called right hemisphere LD or nonverbal LD, it is often associated with deficits in social perception, often comorbid or confused on differential diagnosis with ADHD, and often presents late, usually when abstract mathematics demands increase in late middle school or high school (or sometimes much later in a high cognitive child like your daughter). Sometimes there are physical coordination issues, too.
Every year I evaluate at least a few children who have either managed to get by until they reached the secondary level, or were on an IEP in elementary school, but dismissed at the beginning of middle school, before they hit the hard stuff. (In some individuals, there are early delays in reading, which resolve once decoding itself is mastered, and academic demands switch to comprehension. If this happens before math becomes abstract, they look like they're out of the woods, and are no longer eligible for an IEP.)
One caution about evaluators: not all evaluators (especially academic learning specialists; most psychologists will be fine) are familiar with NVLD/RHLD. I would suggest feeling out the school a little if you decide to try testing through the school, by experimentally bringing up NVLD as a concern of yours. If you get a blank look, find a private evaluator who knows about it.
Schools are not required to accept the recommendations of private evaluations, but they are required to consider the results.
Another route you can take is to have the district do the testing, then ask for an independent evaluation (at their expense), if you don't agree with the results of the testing, or believe that they are invalid for specific reasons. The district will have to approve your private evaluator (since they're paying for it), but there is no obvious reason they would object to a licensed professional with a legitimate practice or hospital affiliation. The other condition is that, since they are paying for it, they have a right to the results. So if you don't believe those results are representative of your child, you will not have the right to withhold them from the school.
