Like Lyra Belacqua in The Golden Compass, the four March sisters are left in a fatherless state, because Mr. March is working as a Civil War chaplain, and, although they have a loving mother, they must in many ways make it on their own. Both the March girls and Lyra are faced with a moral universe in which they only thrive by making the right choice between good and evil. The March girls are guided by the book The Pilgrim's Progress Marmee gives them for Christmas (as well as by Marmee herself), while Lyra relies on the truth-telling instrument called the alethiometer. Both Lyra and the March sisters live in a "fallen" state: the Marches once had more money, and Lyra, though the child of nobility, is not recognized as such.
Jo is closest to Lyra, as both are stubborn, self-willed, athletic tomboys who like to take matters in their own hands. In Little Woman, there is tension between pleasing oneself and pleasing one's parents or adult figures, and we see this most pronouncedly in Jo, who struggles with conforming to being a young lady. Jo is the one who also most directly challenges gender norms: she likes to play males roles in dramas, she sells hair to earn money so that her mother can go to Washington to see their father, and she is bold about seeking a living as a writer.
Because Jo is also such positive character with whom many readers identify strongly, we can see that Alcott uses her to challenge the Victorian idea that women should be passive and prissy. At the same time, domestic women like Beth and Meg uphold stereotypical gender roles.