Failing that, is she based on or similar to any characters in folklore of the region?
As far as I know, the extraordinarily compelling children's character was purely an invention of the author, Astrid Lindgren, but the giantesses in Norse Mythology, for instance, could be seen as a precedent for Pippi's incredible strength which so impressed and delighted me as a child.
(I will have to start by apologising, as I will only quote sources in Swedish for this).
Vivi Edström, in Vildtoring och lägereld, analyses several of Lindgren's books. A lot of space is given to Pippi. The part that comes closest to the question is just one sentence: "That a child is stronger than an adult is a motif from myth", but she also notes how Pippi is really not a mythical type of character.
Furthermore, she notes how Pippi in her first incarnation (a manuscript that was submitted but not selected for publishing) was mainly an absurd figure, and how the story was filled with nonsense verse, paroding Swedish culture. Pippi's strength, and use of it for good, was more developed in the revision.
A few other aspects we have more sure sources for. The official page for Lindgren notes some inspirations: her red hair and freckles came from a classmate of Astrid's daughter Karin (whom she first told the story to). A young girl living alone in a house with a horse on the veranda was apparently a feature of Furusund, where Lindgren spent summers.
Another big inspiration for Pippi was Anne of Green Gables. This is also noted by Edström, and further here.
I will have to finish by saying that, analysing Lindgren's books for influences in general is often very rewarding. There are pieces from classic Swedish Romantic poetry, folklore, Shakespeare, and everything in between, and that is just the fantasy books. Norse mythology is however, at best a minor influence: the fantasy stories are more oriented towards medieval ideas.
