I'm 5'11", OP. I grew a foot in eighteen months over the course of years 8 and 9 but, as others have said, didn't grow much after I started my periods at 13 and a half.
I did find it awkward during my teens, especially before most of the boys had caught up (!), and I do sometimes feel sad that I'll never be "cute" or delicate - it's hard to feel feminine sometimes when you're tall. Like your DD I am/was a swimmer so although I'm slender I have broad shoulders, which adds to the feeling of being enormous I sometimes get!
That said, the advantages outweigh the disadvantages, in my opinion. I'm strong, I'm striking, I do elegant very well when I put my mind to it. And I can always see at concerts and reach the top shelves! As a teacher, having an imposing physical presence is also quite a useful tool.
I have never really got used to wearing high heels and can't walk in them because they hurt my feet - if your DD thinks she would like to wear heels at some point in her life then I genuinely recommend she gets a pair to practise in now, even if she only wears them at home.
I think when you're tall it's important to find your style and make sure you dress to suit your figure: I can't do boho because on me it's more mad cat lady than girly and adorable, for example.
She will feel better once she gets to sixth form and most of the boys have finished (or started) growing, but I would really encourage her to own her height and make a feature of it, rather than slouching and trying to hide. Tall girls rock!