At 1 year old, board books are good. My 10-month old newphew LOVES "Brown Bear, Brown Bear", "Good Night Moon", "The Little Mouse, the Red Ripe Strawberry, and the Big Hungry Bear", and others like that. Books where the pages can be turned quickly and the child can "point to the duck" or identify things are really good for that age, too. If she likes animals, there will be books like that for identifying animals (and making animal sounds), as well as ones for shapes, trucks, etc.
For Duck books, you HAVE to look at "Click Clack Moo Cows that Type" and "Giggle Giggle Quack" and that series. Yes, the first one is about cows, but the duck starts the whole thing http://www.amazon.com/Click-Clack-Mo...8236542&sr=8-1