So you know all about Pippi, and undoubtedly also Ronia the Robber's Daughter, which is even better (for slightly older kids.) But I'll mention Ronia anyway, for other people who might be reading this thread. It's one of our family's all-time favorites.
Some other chapter books with brave girls having adventures:
Coraline - Neil Gaiman
the May Bird series - Jodi Lynn Anderson
Igraine the Brave - Cornelia Funke
The Night Fairy - Laura Amy Schlitz
The Silver Crown - Robert C. O'Brien
The Princess and the Goblin - George MacDonald
The Mysterious Benedict Society series - Trenton Lee Stewart (2 of the 4 main characters are girls, including the bravest one)
Swallows and Amazons - Arthur Ransome (features both boys and girls, but the girls are as brave and competent as the boys)
Coraline, The Silver Crown, and the May Bird series are all potentially too scary for young kids, but they were big hits here. My kids were ready for them at 6 or younger, but some kids wouldn't be.