I am a child psychiatrist, and I can't diagnose a child I have not done an evaluation on, but she is showing the classic symptoms of Attention Deficit Disorder, Inattentive Type, the most common type diagnosed in girls. There is almost no hyperactivity. They are never a behavior problem in the classroom. They daydream, can't start or finish work, are too social and are interested in what everyone else is doing. They can focus on what they love to do, like her at home reading. In a quiet, non-distracting environment, they can focus better and get work done. Get an evaluation from a child psychiatrist or psychologist. There are more things you can do besides medication, but medication is the most effective intervention for most kids.
A little about me: Married 21years to a supportive husband and great father, two kids with ADHD, a 19yo boy and 13yo girl, both doing well in school (my son didn't do well until college, where he is doing what he wants to be doing.)