LOL, I get a kick out of TLTWATW as a first book! That's great!
My oldest dd was a stealth reader. She has perfectionist tendencies, and she doesn't like to show what she knows until she feels competent with it. So though I know she was reading individual words at age one, I never got a good handle on exactly when she started really reading. It was when she was two, but probably a mid to late two. I call this the Michigan J Frog syndrome. She'd read all the words on the computer screen to play Reader Rabbit kindergarten, but then my mother would ask her to read a BOB Book and she'd freeze like a deer int eh headlights. My mom was convinced that I was delusional, and said things like, "You know dear, it's ok if she isn't reading as early as her brothers..."
I believe that with this kind of child it's important to talk about the steps of learning, how everything gets easier with practice, and to let them see us struggle once in a while trying to master something new. This same dd wrote her name for the first time when she was 2.4, but was unhappy with the appearance of her letters (they were legible, though) so she refused to write letters again until she was three.