Once my daughters could handle the easy readers, they were now ready for chapter books. A librarian suggested The Boxcar Children by Gertrude Chandler Warner as a good starter series. My daughter loved these books about four resourceful children and their adventures. Another good chapter book series is The Magic Tree House by Mary Pope Osborne. And who could resist the Nate the Great books by Marjorie Weinman Sharmat, great mystery books about a boy detective and his dog Sludge.
Magazines can be a good source of reading material.
She felt very grown up getting her own magazines and we'd read each one as soon as it arrived.