While it seems to be very, very common for highly gifted kids to be dissatisfied with a conventional school environment, it is not universal. There are a few families on these forums with kids who are pg but happy with their age-peers in schools that do not specialize in gifted children.
If I were you, I would definitely go forward with the WISC-IV for the following reason. If she is highly gifted, there is a good chance that she does very well in school with minimal effort. A problem can develop over time if a student does not associate learning and doing well with persistent effort. Perfectionism and other related challenges have been well documented on this forum. It is far easier to address this early on by seeking an environment where a child is truly challenged than to deal with the perfectionism, etc. later on.
(My own dd is now 13 yo and has always scored exceptionally well (even by gifted standards) on standardized tests (Explore, MAP, SAT). She attends a neighborhood public school and has never had a full grade acceleration. She is quite happy with her circle of friends at school, and academics at school have worked out okay so far due to some great teachers (although this is hit and miss), subject acceleration in math, some accommodations in other subjects, and engaging interests outside of school.)
