Movement of words and letters is a definate sign of LD. and yes you can be LD and gifted. She would need to be evaluated by someone for an official diagnosis. There are some who think that if they are at grade level is enough.
Some quick things to try to alleviate reading can be using a transparent colored overlay over text. You have to try several different colors to find out which works best. It stops the intensity of black on white contrast. I had a student who wore cheap rose tinted sunglasses to read. A cheap way to get the overlays is using the thin plastic folders that can be dividers for a binder.
Has she tried keyboarding? It helps many kids with these issues.
Good luck and stand up for your child. when mine was threatened w/ removal from gifted pull-out I made them wait until assessment was done and accomadations had been met. It worked well. My DS9 dictated to an aide(hser) who writes down what he says. Needs met and teacher sees him for who he is