I think go where your child leads. I was taught very young (think mum started to teach me when I was 2.5 years old) and at that age I was desperate to read apparently. I don't think it did me any harm and I spent most of my childhood lost in a book (yes, I got to choose my own reading material - and at the age of 8 I would choose about 25% adult fiction - i.e. everything on my parents' bookshelves!) My mum had a major argument with the librarian once because a child's ticket was only 4 books and I was getting through them in an afternoon and wanting to go back next day. Eventually they gave up and gave me an adult ticket (8 books a visit).
Despite some of the "horror" stories, I didn't struggle at school even though I was ahead. I was lucky in that I had a sympathetic teacher who would let me "skip" readers (which were boring topics anyway - wouldn't bother reading them out of boredom, not from lack of understanding) and let me choose from the school library.
Ds at the age of 2 is already exhibiting similar behaviour traits - if he could choose to, he would have me read to him most of an afternoon. He's constantly pointing at letters (on t-shirts, signs, etc) saying "wassat, mummy!". He loves his pop-up alphabet book and number book. He brought me a recipe book to read to him the other day because he like the look of the pictures! I can see him becoming an avid reader and I can see me teaching him to read early. I've already started to read up on various reading schemes to make sure that if asks me questions I won't tell him anything that'll confuse him later. (After all, I don't want to deliberately set out to make his future teacher's lives difficult!)
In reality I started teaching him to read from a baby. He knows that there's a story in the pages, that you turn over the pages to get to the next part, that the pictures help tell the story too, that there are odd squiggles that mummy scans from left to right to tell the same story over and over again. He recognises the Weetabix symbol and the Number 1 (as that's the number painted on Thomas the Tank Engine). See, already I've been teaching him. Evil Mummy.
I can understand the idea that you shouldn't push your child before they are ready. However, I will not be deliberately holding my child back despite his obvious interest. The second he's bored with it, I'll stop completely until he's asking questions again, but I'm not going to avoid his questions just because of some survey says that dire things are going to happen if you teach them to read before the age of 6! And no, my child will not miss out on play and childhood because of it. To him reading is fun and is play. Some of my best memories as a kid is of me half way up a tree reading a book.
Trust your instincts. If your child is eager, gently introduce them. Read up yourself on different schemes, take it slowly, test the waters, and if they're still keen to learn more don't stop! You know your child far far better than anyone else does. If you listen to them and listen to your judgement I don't think you can go far wrong.