A couple comments--
First, I really love private testing, because you have control over the date/time (time of day is very important for some kids, like mine). Also, frequently the in-school testing setting can be noisy or have distractions. So, if you can afford it and find they'll accept it, maybe that's one way to decrease anxiety.
In NM, we have to go through a "re-evaluation" every so many years...maybe 4 years? I don't know exactly. The teachers can require re-testing at that time, presumably based on the performance of the child (since your child is doing above level work, I would think she would not be a candidate for re-testing here). I almost wish my oldest son were recommended to be retested, just for curiosity sake (certainly not enough for me to pay for it), because his original test was before he could read, and the whole world opened up to him after that--so I bet his real IQ is much higher. I guess one way to present it to your child and how I would with my kids is as an opportunity. My kids love testing. They ask me to seek out above-level testing opportunites like SCAT, PLUS, EXPLORE, SAT, ACT, etc. If there is so much anxiety associated with testing, maybe you should have her do many, to increase her comfort level. My 11-yr old son took the ACT/SATs last year. He scored higher than I did when I was 17 and applying to colleges! I thought that if I had had the chance to test early/young and do it several times so that I didn't become out-of-proportion anxious about it (I remember thinking that my whole life, my whole future depended on this test), maybe I would have relaxed and done better. Plus learned some test-taking strategies. These tests are important ultimately regarding scholarships, college choices, etc., so practice is worthwhile.