I too am an avid reader, and understand your eagerness for her to share the world of books. But I'm going to respond by telling you a little story from a different field of joy.
Music has always been a very big part of my life, and a source of much delight, both as a listener and as a creator. So I started teaching our kids piano when they were very young. Our oldest showed early signs of both interest and talent, but adamantly refused to sit for any kind of instruction until a very specific self-determined (although very appropriate beginning lesson) age. Even before that (exact) date, they spent copious amounts of time sitting at the piano, playing, singing and composing. But for years, it was a struggle to teach specific pieces (either sung or played) to them, and they practiced only because of their compliance. All the while, hours were devoted to their own material. Eventually, I gave up on formal instruction, figuring that sufficient basic technique had been conveyed (if not the classical repertoire that I love and would have liked to share with them), and let them play and sing whatever they wanted, which turned out to be mostly things in their own head--which is the point at which their skills really began to take off. After which DC started picking out advanced classical pieces on their own to learn, and even (gasp!) occasionally asked me for technical tips.
In case you're wondering, the point at which I released my ambitions for lessons was when DC had enough proficiency to progress independently (so, able to read music--if slowly, solid finger technique, probably late elementary-level pieces), but wasn't necessarily at an advanced level.