It's not so much that the FSIQ should/should not have been calculated, as that it doesn't fully capture her range of abilities. How were her other index scores (if they were calculated--if not, if you don't mind sharing her subtest scores, I may be able to comment on her overall profile)?
Anxiety can affect any scores, however, her achievement score profile does back up the piece of the cognitive profile you reported, which suggests that, even if there was some underestimation, the FRI > VCI probably represents a genuine cognitive difference, rather than purely anxiety (which one would expect to have wider-ranging effects, or to affect math, working memory, or processing speed more). Reading in the HA/S range, though definitely above grade level, is not necessarily in the GT range for reading. (Though her math scores are excellent.)
How are her writing skills?
