Yamibo: Darkness, The Hat and the Travelers of the Books

Hatsuki is a highschool student living with her sister, Hatsumi, who she has a huge crush on. On Hatsumis 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 stored in books. Hatsumi wasnt there, though, so the search for Hatsukis great love begins and involves traveling from book to book.