I would bet that this was a reference to the 1919 novel A Woman's Woman by popular writer Nalbro Bartley. It tells the story of Densie Plummer, a thirty-seven-year-old mother of three who's dissatisfied with her life.

It was during her elder daughter Harriet's high school graduation in 1901 that Densie Plummer determined after nineteen years of unquestioned loyalty to break up her home and start life anew in strange and contrasting channels.

Densie's problem is that she's rather old-fashioned, a simple and motherly woman in a modern world. Her oldest daughter, Harriet, wants her to be smarter and less emotional. Her second daughter, Sally, wants fashionable dresses and fun. Little Kenneth is starting to grow up and not want his mother to baby him. Her debonair husband, John, is frustrated with her frumpy, practical clothes and her homemaking. Finally, Harriet strikes out and attempts to modernize, but it's a failure: she visits Harriet at college in New York City, but Harriet is a feminist and labor activist with a bob and pants who has no time for her. Densie and John go out for dinner and a show with another couple, and the other wife shows her up in both dress and manners. On her return home, she finds that Sally is being (willingly) courted by a much older, wealthy man without any care for her parents' consent. The world continues to pass her by and find her wanting.

By the end of the book, the narrative has caught up to the writer's present. John is unemployed, and he and Densie no longer have a house of their own. Sweet little Kenneth has grown up and gone to fight in WWI, where he is shot escaping the guardhouse when being punished for overstaying his furlough, and dies. Sally, married now, confesses to her mother that her older husband is actually a German spy. Harriet suffers a nervous breakdown. Densie gets them all a new home to live in and makes it warm and comfortable, and they all realize the value of her plain practicality and old-fashioned homemaking talents.

The title comes from a bit near the end:

She did not know Densie had resigned from her public interests and to a delegation of protesting citizens she had said quietly: "My family needs a home, and a home must have a home maker and keeper, one whose first and last interests and devotions are given to its welfare. There can be no halfway. As the stone age man left his woman beside the cave to keep the fires aglow and thus ward off wild beasts, so the man of to day and the woman of business - for there must be women solely of careers and business in to day's scheme of things - must leave in their dwelling some woman's woman who will keep the fires aglow and ward off modern but equally wild beasts!"

We do have the common phrase "a man's man" ("Catcher Block - ladies' man, man's man, man about town"), which basically means the kind of man that other men like/are impressed by, and we could draw an analogy here to suggest that a "woman's woman" is a woman that gets on better with other women than with men, but honestly in the scope of the novel that doesn't seem to be the case with Densie. This is more figurative - a woman who is wholly "woman" (by an antiquated set of gender norms) and doesn't cross over into public life, a career, overt sexuality. You might think that in the 1910s, that would be fairly uncontroversial, but even by then a woman who was solely interested in homemaking was seen as regressive and unappealing - though, as the novel points out, many men still wanted a wife who was frilly and made a good pie crust even while being annoyed that she wasn't more fashionable and modern, a double standard that couldn't be resolved. I have an answer on the fall of the Age of Domesticity to fill in the background there.