Transcendentalists held progressive views of women, and they believed that people should consult their own consciences in making moral decisions. Both of those aspects of transcendental thought appear in Little Women.
Part of Little Women's enduring popularity comes from the way the March sisters, especially Jo, earn their own living and pursue their own paths. Their father, away as an army chaplain in the Civil War, doesn't earn much money, so Marmee, Meg, and Jo go out to work. Jo might complain about her hours as a companion to the grouchy Aunt March, but she is contributing to the family livelihood. More importantly, Jo has inspired generations of women writers in her unabashed pursuit of a writing career, publishing pot boilers and Gothics. Professor Bhaer might not like what she writes, but Jo is a young woman who, like Margaret Fuller, can earn her own way in the world through her pen.
Meg initially earns a living as a governess, and Amy pursues a vocation as an artist. The book praises this spirit: when the March sisters meet Laurie's British friends, who scorn women working, they are proud to assert their American (and, we might add, transcendental) independence.
While the frame of the girls's the spiritual journey to womanhood is the volume of Pilgrim's Progress that Marmee gives them for Christmas, they are not asked to follow any particular denominational theology or consult with a pastor for moral guidance (in fact, they never seem to go to church at all): they are, instead, repeatedly expected to examine their own consciences to determine the right thing to do.
Not surprising, Emerson, whose Self Reliance advocated just that, was Alcott's Concord neighbor. The girls, from Meg when she visits "Vanity Fair" to Jo when she is challenged to forgive Amy for burning her manuscript, are expected to find guidance from within—though Marmee is always there as a sounding board to fall back on.
Louisa May Alcott, author of Little Women, was herself a transcendentalist. Many of her neighbors in Concord, Massachusetts were also members of the movement, including Ralph Waldo Emerson, Henry David Thoreau, and Nathaniel Hawthorne.
A great example of the transcendentalist philosophy in the story can be seen in Meg's decision to marry John Brooke in open defiance of existing social conventions. John hails from a poor background, so his marrying someone like Meg would've been frowned on by respectable society.
Like the good transcendentalist she is, however, Meg's not interested in any of that—she has her mind fixed on higher values. She wants to live a simple life, a life lived in accordance with nature. Among other things, this means listening to her heart instead of blindly following societal norms and values. As her heart tells her that she loves John, she decides to marry him. Meg loves John irrespective of his background, and in keeping with her transcendentalist worldview, that's all that really matters.
In Little Women, the March family recognizes the power and importance of being in nature. Marmee routinely insists that her daughters go outside, and so they have created their Busy Bee Society, where they take their work and go outside to do it. They climb up a hill where they can see the countryside around them, and it makes them feel more centered, calmer and contented. Laurie, also, feels the healing effects of nature; after he's had an argument with grandfather, he goes outside to rest in the hammock. He finds that this time outside quiets and calms his mind as well. The emphasis on the healing effects of nature is very transcendentalist.
Further, when Marmee allows the girls to conduct their experiment (where they will do no work for one week), the outcome is a very transcendentalist one. When they do no work, the girls find that they become very bored, and they begin to enjoy their lives less. Food isn't prepared, the house is a mess, the girls no longer enjoy the things that once brought them pleasure, and even little Pip (Beth's bird) dies because Beth forgets to feed him. At the end of this time, the girls learn, as Marmee says, that no work and all play is just as bad as all play and no work. There is a satisfaction that comes with doing a job well done, with doing what needs to be done as well as what one wants to do -- really, the scenario points out that we should want to do what needs to be done and, in this way, it takes on new meaning and purpose and we no longer resent it.