My son had his first IQ test at age 5. He scored above 150 on the verbal portion, but below 90 on the non-verbal portion. He came out with an FSIQ score of around 116, which was only 1 SD above the mean for that test. He was later tested on a different test. His Verbal IQ on that test was at the 99th percentile, his non-verbal score was at the 50th percentile, and his processing speed was at the 2nd percentile. Not surprisingly, his FSIQ was, again, only around 1 SD above the mean. The FSIQ on these two tests was a terrible measure of his IQ. The index scores gave a much better picture of his abilities and disabilities. The psychologist who tested him the first time indicated that he had obvious non-verbal disabilities, and the Verbal score alone was the much better measure of his intellectual potential. (The person who administered the second test was not a psychologist, just someone that the school system had "trained" to administer and score the test, not assess its implications.)
It is possible that your child has some subtest scatter either within the subtests on each index or between her index scores, and it is this scatter or variability that brings her FSIQ down to "only" 1.5 SD above the mean, or it is possible that she is a very motivated person with an IQ of 122 - which is pretty close to the mean IQ of physicians and Ph.D-level scientists, so it is nothing to sneeze at.
