The Wishing Star (Starlight Trilogy #1) by Marian Wells

Jenny, living in the frontier districts of New York and Ohio in the early 1800's, is a bright and unusually inquisitive young girl. Though surrounded by poverty, enduring abuse by a drunken father, and in spite of limited schooling and spiritual guidance, curious and quick-minded Jenny reaches out for something different. The window out of her restricted life is the world of books. The green-covered one, her father's forbidden book, holds an overwhelming fascination for her. Will Jenny find truth, or is she on a dangerous road with no end in sight.