Sorry, so I guess I'm wondering, do parents of kids with this kind of score normally also do an IQ test?
I'm not sure on that one. We've done both with my dd10 and her IQ scores were significantly higher than her CogAT scores but her CogAT scores weren't nearly as high as your dd's. And, thanks Dottie for the further info. I don't feel chastised

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My thought would be that I'd tentatively assume that she's gifted to some degree but not put a pin on the board as to where exactly that falls at this point. Even kids who are retested on the CogAT or other school ability tests tend to see some changes from year to year and sometimes significant changes. If she seems to be performing significantly above grade level and you cannot get appropriate acceleration for her with the scores you already have, I'd consider further testing then.
We have one child for whom we probably don't have a really good pinpoint as to where she falls in terms of the gifted spectrum but my bets would be on HG. Her one ability test was an IQ test done at age 7 after coming out of a really bad prior school year. She froze, refused to do parts of the test at all, and generally had wildly erratic #s across the test, but she was still somewhere in the gifted range. We were told to retest her later, but we never have. Her achievement since then has been so high that she's gotten mostly what she's needed without further testing.