My son has similar problems to your daughter and he is also gifted. There is a thread about it on 'need help with scores'.
My son has vision issues even though he has 20/20 vision. The latest info I received on his problems is this:

"I took my son to a vision therapist. He did 2 hours of testing. There is a problem with his vision. He is reading at a speed of 13th grade level, however his brain is turning on and off each eye rapidly. He is rarely able to use both eyes at the same time although he has perfect vision. When his brain changes eyes, it leaves gaps between letters in his writing, he misses words when copying things, and also when reading. I will get the full report on the 22nd, but it looks like his low processing speed is due in great deal to his eye problems. They gave him a test which had him see with his right eye the number 4 in line over a vertical dash, and his left eye saw a horizontal dash in line over a 2. If you see with both eyes it would look like 4 + 2 (vertically). However, he saw them separately and could not put the different dashes together to make a plus sign. Could be why he hates math worksheets, but is phenomenal in math as long as it is mental math. Things don't look like they should...maybe it is a minus sign, maybe it is a plus sign...columns don't line up.
Just thought I would update you in case anyone else has similar problems/test scores, with a child who has had strabismus/amblyopia issues."

He has had 2 surgeries and had seen a different vision therapist when he was 4-6 years old. My son was telling me he was seeing fine, which technically he does see fine. However, his brain turns off one eye and then the other. He leaves problems half done etc. Excellent speller but math facts/timed math papers he is horrible. He knows his facts but can't do them quickly when looking at them being flipped or on a timed test. He does all his math mentally. I hope you will consider a vision therapist to rule out vision problems that can't be seen by the regular eye exam. They can test your kid with goggles to measure where her eyes are tracking while reading etc. The fact that your kid can't focus or concentrate was the exact reason my kid was sent to be IQ tested. They thought he was ADD/ADHD. Turns out he isn't (he has had the test twice). My son also leaves problems half done, skips problems, leaves letters out of words when writing that he knows how to spell, all because he is not seeing properly. He actually tested >99% on spelling during the testing for ADHD (WIAT II). This year in 3rd grade my son had been going to the teacher for 'help' with his math immediately after she gave directions and told them to get started. He would tell her he didn't get it. She would tell him to read the directions out loud. As soon as he did, he immediately understood and could whip out the math paper. It turns out, my son is an extremely good compensator for his vision problems. He has learned to compensate by turning his visual processing problem into auditory process that he can understand, by reading out loud. He then doesn't have to rely on what he sees. Who would have known? He doesn't follow directions well and it drives me nuts. He too may have a LD. We will hopefully know soon.
Good luck to you!

By the way the optometrist/vision therapist told me that ALL but 3 of the signs of ADD/ADHD are also signs of vision issues.