C.V.
I have ADHD, and so do my kids. I do have experience in the evaluation process. But based on your post, I don't see the need for an evaluation or any reason to assume that your child is anything but a neurotypical child.
Your child's teacher stated that she doesn't think your child needs to be evaluated, that she needs to work harder. Why don't you start there, with her work ethic, and see what happens? Help her to buckle down on studying, talk to her about checking her work and using every minute of testing time to do so.
I'm confused as to how you go from "she tests on the PIAT at or above grade level" to "she's rushing through her tests and getting low scores" to "she needs to be evaluated for ADD," which is NOT a learning disability, by the way.
Nothing you've told us indicates that she needs to be evaluated.
ETA: Oh, and there's no miracle vitamin or diet cure for ADHD. For allergies and food intolerances, yes, but not for ADHD.