YAMIBO: Darkness, the Hat, and Travelers of the Books

Yami to Boushi to Hon no Tabibito

Hatsuki is a highschool student living with her sister, Hatsumi, who she has a huge crush on. On Hatsumi's 16th birthday, she is suddenly surrounded by a green light and disappears in front of Hatsuki. She manages to follow Hatsumi with the help of a being resembling a fat baby chick (literally), ending up in a place called "The Great Library", which is full of different worlds...