In order for parents to collect benefits, a child needs to be severely disabled and several grade levels behind in developmental areas (academic and life skills). This is usually meant for parents who's child is so severely disabled that they can not work, need to provide constant care/supervision and encounter many medical bills due to the disability.
You daughter will most likely not qualify as this reading disability does not several limit the things she can do.
From the SSI website:
"The child must have a physical or mental condition(s) that very seriously limits his or her activities"