I'm reading a book called Raising Confident Readers by Richard Gentry right now. The author argues that writing usually comes before reading so it sounds like what you describing is pretty normal.
Interesting... my DD started writing letters at 26 months (just upper case with straight lines - she hadn't mastered the fine motor for curves yet) and this was just two months after she started talking, so... she hadn't demonstrated word reading ability yet at that point. I honestly can't remember when the word reading started, but by 3 1/2 she was probably at about grade 2 level (contractions, compound words, silent letters, etc.). So yeah, her word reading likely happened after her writing started.
