Some of us are assessment geeks. We want to see the subtest scores before we know whether we can trust the FSIQ. Some school psychs don't use the FSIQ as a summary of the student's cognitive ability if there is a big disparity among the subtests. You're lucky we didn't ask for confidence intervals! I think you may also be mixing in the scores of an academic assessment with the WISC there.

The focus and processing speed may improve as she gets older. Does she often have trouble with focus? You wouldn't necessarily see that kind of frustration with the slow pace of school with an IQ of 120. Personality would play a role, though, in her expressing this to you. I'm going to go ahead and predict that she is a "Feeling-Perceiver" on the Myers-Briggs.
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From http://www.educationaloptions.com/resources/resources_rufs_tips.php

"If they are Feelers (FP), they will feel morally violated when asked to do what they sense is wrong, unnecessary, or demeaning for them. When they are threatened with punishment or bad grades, for example, it not only doesn�t work, it builds resentment and anger in the FP student. One way I suggest for parents to know if their gifted child is an FP is to ask them if these words have ever come out of their mouths: �In the amount of time you�ve argued with me, you could have finished this.� One last word on Perceiver children: the gifted children who are brought to specialists such as me are a parent-selected skewed sample. Although estimates of the percent of the US population who are Perceivers is 48%, a consistent 92% of the children who are brought to me for help are P-Perceivers."
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A couple of possibilities are that this testing is not very accurate for some reason, and that there's a lot more to the story than she is telling you. That the testing isn't terribly accurate is a distinct possibility given her age and state of mind. The WISC report is one piece of data, one snapshot from one moment in time. It should be considered in the context of everything that you know about your child.

You might look for the book "5 Levels of Gifted" by Deborah Ruf. There are a bunch of milestones in that book, and quite a bit of discussion of the different degrees of educational needs of gifted students.