As a mother of an undiagnosed but possibly dyspraxic 12 year old son, I would get her diagnosed! He is very happy go lucky though, I have never felt perfectionism was part of the dyspraxic profile in his case, as he was much too careless.
I probably had dyspraxia, and yet I absolutely loved dancing, and was good at all the things you describe, highly academic, but nevetheless there remains this problem with sequencing/organisation/motor skills that does cause significant difficulties later (at least it did with me). My mum wrote a poem about me aged about 11 which sums it up "Angel child or silly clot! (it was a joke)" 
I think that is how she felt, frustrated at my clumsiness, and yet impressed by all my other talents!
If your child is bright, it can mask the difficulties.
I would say the most significant thing is that your daughter feels frustrated. By something, her own skills, your judgements, school, something. Worth seeing the doctor just to discuss that issue alone: is she stressed by too much pressure on her, too many after school activities, too much homework - if she is a natural worrier, maybe the problem lies in just taking a bit of time to get her to slow down and realise she doesn't have to be perfect, and enjoy things that aren't being judged in any way, reading to herself, playing that sort of thing..
I found I gained a lot of confidence doing craft, sewing and other slow stuff that wasn't competitive, rowing, climbing, walking, singing etc. I suppose a sort of poor man's OT..
Also worth going to Dr just to check anything untoward with the physical symptoms you have described, just to set your mind at rest that there isn't a PHYSICAL cause..the dyspraxia thing might not the real reason she is tripping up etc.