What is her anxiety about? Is it about finding school work difficult, being perfectionist, fitting everything in, stressing about competition with others? Did she get stressed about the transfer test?
Or is it more that she is anxious about new people, new situations, social stuff, fear of future things happening etc?
Depending on the source/type of anxiety, being in a less academic school might not make it go away anyway. I was extremely anxious as a child/teen, and an academic school helped - gave me something to focus on, more chance of finding like-minded friends, more interesting clubs beyond just sports that were the main thing at other schools, not feeling weird for being clever, all that sort of thing. There were of course still many other anxieties that would have been there regardless of school, but choosing a less academic school wouldn't have changed that. On the other hand, I did become very perfectionistitc about things, and the competition at the academic school both spurred me on and made me put huge pressure on myself at the same time, which was stressful - but that should have been dealt with regardless (and wasn't).
So it might be that the academic school is best for her, but that you'll need to deal with some of the anxieties anyway. And in some ways, the grammar school might be helpful for her with like-minded children, not feeling as out of place, etc.