First of all, I would never throw out any good books for smaller children. A book that is good literature is good literature. Full stop. Your dd wants to expand her reading, not narrow it down. Even an adult can learn about good writing from the best picture books.
But for additional reading, I would recommend:
Noel Streatfield, Ballet Shoes.
Cathy Cassidy.
The Lady Grace mysteries.
Rosemary Sutcliff: Warrior Scarlet, The Eagle of the Ninth (and there are plenty more).
The Laura Ingalls books.
Harry Potter. (Not perhaps great literature, but they have been well proven to encourage children to read)
E. Nesbit: Five Children and It, The Amulet, The Enchanted Castle, The House of Arden.
Mary Norton: Bedknobs and Broomsticks (this is imho is a seriously good book!) and The Borrowers.
Norton is one of the best authors (adult or children) I have ever read, for humour, for language and characterisation, for descriptive detail that actually means something. But the Borrowers is quite hard work, because of the sheer amount of descriptive detail.