Hi newtron, you would be amazed at what a 3 year old can do - she does sound bright though - if you read poems to her, she will know which poem it is by the shape it makes on the page - try it!
I hope that she is settling in with you.
I cant recommend reading to them enough, I wouldn't worry too much about teaching her all her letters though, because you will find that when she starts school they will start them all at the same level and she will be bored very quickly. We never pushed either of my boys to read, but read to them every day. Once they started school, they just lapped it up and are already 2 years ahead of their peers at only 7 and 6. I think though that had they started school being able to read, they would probabaly had a very different start as they would probably have just gotten into trouble through boredom.