You won't discourage her! My daughter was precocious with wanting to read, too. And there's no such thing as "too early" if the child wants to. My mother still has her notebooks from her work with her very strict father. She was writing in cursive...shaky, but cursive...and doing long division at five. But when she got old enough to go to school, she was bored. That's one reason so many don't teach kids who want to learn. They're afraid they'll get bored later. Since you're going to homeschool right along, then let her start slowly while her interest is there! Doesn't have to be formal. You can do it while reading to her. Letter sounds. Then start putting them together to sound out words. She's going to be thrilled to be able to read "Cat in the Hat" for herself soon!
