The Rick Riordan books are a great way to get some classical myths into her. He also manages to weave a really diverse set of characters into the books without it seeming forced. My kids devoured these books at your DDs age.
Percy Jackson and the Olympians
The series that started it all. Follow the demigod son of Poseidon and his friends on a quest that will have them meeting gods, battling monsters, and taking on the Titans from Greek mythology.
The Kane Chronicles
When the gods of Ancient Egypt are accidentally unleashed into the modern world, siblings Carter and Sadie Kane discover that they are descended from the most powerful magicians, and only they have the power to set things right!
Magnus Chase
A new demigod is born—this time from Norse mythology. Join Magnus Chase, a homeless boy from Boston, on a wild adventure that will have him meeting the gods of Asgard and discovering his true identity.
Trials of Apollo
After angering his father Zeus, the god Apollo is cast down from Olympus. Weak and disoriented, he lands in New York City as a regular teenage boy. Now, without his godly powers, the four-thousand-year-old deity must learn to survive in the modern world!