There are Little House series extensions written by other authors. They are prequels and sequels to the books that Laura wrote. They are called The Caroline Years (about Laura's mom), The Rose Years (about her daughter, Rose Wilder Lane) and so on. I have no comment on the quality of these books because I've never read them. DD enjoyed a few of them though but she was never a huge Little House fan.
You may also want to try Caddie Woodlawn by Carol Ryrie Brink.
I would also highly recommend The Birchbark House and other books by Louise Erdrich, telling the story of a young girl in an Ojibwe tribe around the same time as the Little House books. There is some tragedy in the book, so it may require some caution for very young readers.