otherhood
n. The state of being a woman who is not a mother; women who are not mothers collectively.
Examples
2014
Among the salient findings of the study, women of the "otherhood" are "thriving career-wise," and 75% of them had some college education or above, compared to 67% of women with kids, according to a report on the research.

Indeed, "otherhood is a sign of social progress … and empowerment," said Hannah Seligson, a contributor to The New York Times who has become a voice for Millenials and collaborated on the study, during a recent panel discussion in New York on the topic.
2014
We have gone without definition or visibility for too long. I am offering "Otherhood" as a name for our misunderstood group of women doing our best to live full and meaningful lives despite the frustrations of some of our most cherished Iongings. We, the Otherhood, who have yet to find our rightful, equitable, requisite place in society, deserve one. Our otherhood denotes our state. our condition, our character, our nature, and our tribe.
—Melanie Notkin, “Otherhood,” Seal Press, February 25, 2014
2007 (earliest)
Motherhood versus otherhood is the battle at the centre of Georgia Fitch's personality packed but lightweight investigation of the modern woman, I Like Mine with a Kiss….

Two best friends embody two sides of the issue. Annie is a single parent who defines herself by her motherhood. Aligned against her is Louise, a mess of feminist theory and self-hatred who spurns the idea of childbearing.
—Kieron Quirke, “Mother of all battles over motherhood,” The Evening Standard (London), February 19, 2007
Notes
IV. "The Joys of 'Otherhood'": A Hearing of The Joys of Motherhood.
—Cynthia Ward, “What They Told Buchi Emecheta: Oral Subjectivity and the Joys of 'Otherhood',” PMLA, January 01, 1990