We started chapter books with my DD when she was a 3+. She loves all books... picture, short story, poetry, novels, etc... But I started reading novels to her out of my interest and also to create a more focused bed time routine. It's been a great success. She doesn't like anything scary or suspenseful so maybe our list of successes might be useful to you if you decide to try a novel for your DS.
Beverly Cleary's Henry Huggin books. We read all of them and both really loved them.
The first _Mary Poppins_ by P.L. Travers but I found the later ones very annoying.
Mr. Poppins Penguins
The Wind in the Willows
Charlie in the Chocolate Factory (but she was scared by the Glass Elevator so we put it down)
I'm sure there are others...
Our less successful attempts have been:
My Father's Dragon -- she was impatient to meet the dragon!
The Glass Elevator
The Return of Mary Poppins
and the Ralph Motorcycle books-- she was upset when the mouse got trapped. I'm hoping she'll let me try again though as we had such success with the Henry Huggins books.