I bought my second daughter “Small” by Jessica Meserve, it is a story of a younger sister with an overbearing big sister and how they come to a point of mutual respect.
She also adores “Zero” and “One” by Kathryn Otoshi, the characters are genderless, Zero is about Value (both numerical and personal), One is about bullying and colours, it is the only bullying book I have ready where the bully is reinstated into the group at the end, it’s awesome!
Also have a look at “Pearl Barley & Charley Parsley” by Aaron Blabey – they are opposites, but match perfectly as friends because they care about eachother.
In chapter books: I’m reading all the “Ramona” series to Miss 6, she is loving them, they almost supplant her passion for “Milly-Molly-Mandy”.

Um, hello, Pippi Longstocking? She’s only the strongest girl in the world, full of wisdom and confidence:

“The children came to a perfume shop. In the show window was a large jar of freckle salve, and beside the jar was a sign, which read: DO YOU SUFFER FROM FRECKLES?
‘What does the sign say?’ asked Pippi. She couldn’t read very well because she didn’t want to go to school as other children did.
It says, ‘Do you suffer from freckles?’ said Annika.
‘Does it indeed?’ said Pippi thoughtfully. ‘Well, a civil question deserves a civil answer. Let’s go in.’
She opened the door and entered the shop, closely followed by Tommy and Annika. An elderly lady stood back of the counter. Pippi went right up to her. ‘No!’ she said decidedly.
‘What is it you want?’ asked the lady.
‘No,’ said Pippi once more.
‘I don’t understand what you mean,’ said the lady.
‘No, I don’t suffer from freckles,’ said Pippi.
Then the lady understood, but she took one look at Pippi and burst out, ‘But, my dear child, your whole face is covered with freckles!’
‘I know that,’ said Pippi, ‘but I don’t suffer from them. I love them. Good morning.’
She turned to leave, but when she got to the door she looked back and cried, ‘But if you should happen to get in any salve that gives people more freckles, then you can send me seven or eight jars.’”

Rosie revere engineer is my fave!

The Paper Bag Princess (by Richard Munsch), as well as Bedtime for Frances (and the other Frances books by Russel Hoban). My daughter (3 now) has also enjoyed the Maisy series (by Lucy Cousins), though those are definitely for the toddler/preschooler crowd.

For my baby shower, I requested that the guests give a book for my baby girl’s library rather than a card… My friends and family totally ran with the idea. The number of books we received was amazing, not to mention the fact that there wasn’t a single repeat!
Our favourites with female protagonists:
Laura Ingalls Wilder’s “Little House” series box set
Red Is Best by Kathy Stinson
The Tea Party In The Woods by Akiko Miyakoshi
Mama, Do You Love Me? by Barbara Joosse

Please don’t forget The Paperbag Princess… it’s a lovely little feminist story. A must-read for any toddler and his or her parents!!

I’m sure it has already been listed in older comments, but Brave Irene is a must read for young girls. It still makes me cry every time I read it and with two girls of my own, it will be read many,many times!

Paper Bag Pricess is an absolute must!

Ada Byron Lovelace and the Thinking Machine by Laurie Willmark. This is a gorgeous, brand new book about the first woman coder! The publisher is a small Berkeley press that does amazing children’s books, and all are printed in the US.

http://www.crestonbooks.co/static/ada.html

Hazel’s Amazing Mother by Rosemary Wells

My kids loved Yo Vikings! by Judy Schachner (probably better known for her Skippyjon Jones books) about a little girl who buys a real viking ship and sets it up in the back yard. Fantastic story for girls and boys!

There’s a great website called “A Mighty Girl” which has hundreds of titles of books with empowering female leads, for girls of all ages! Well worth a look!