What type of feminist was Willa Cather?

There are multiple ways to categorize feminism. The most common, outside the academic context, is in waves (first-, second-, third-, and fourth-wave feminism), based on time period. By virtue of time period alone, Willa Cather would be considered a later first-wave feminist, as she wrote during the early twentieth century.
Judith Lorber identified three categories of feminist discourse: (1) gender reform feminism, rooted in the liberal political philosophy's emphasis on individual rights; (2) gender-resistant feminism, which focuses on behaviors and group dynamics that subordinate women; and (3) gender revolution feminism, which seeks to deconstruct social categories and analyze cultural reproduction of inequalities, thereby disrupting the social order.
Willa Cather did not claim any of these labels, and one could make an argument for any of them. O Pioneers! could place her in the gender reform camp—O Pioneers! focuses on Alexandra's individual relationship with tending the land: "it is in the soil that she expresses herself best" (63); "her mind was a white book, with clear writing about weather and beasts and growing things" (205). In doing so the book comes from the perspective of an individual's right to subvert gender norms. O Pioneers! could also situate Cather as a gender-resistant feminist, as Alexandra has to battle against the social norms and dynamics that would keep her from running a farm.
Feminist criticisms of Cather's work often focus on her use of male narrators to describe women's experiences, thereby robbing the female characters of their own voices. In doing so, Cather operated within the confines of a male-dominated literary culture, which would undermine arguments that she advocated for the deep social structural change advocated by gender revolution feminism.
Cather's personal life, however, could be considered a greater subversion of gender roles. For a time, Cather presented as a man and took on male names. There is speculation as to whether this represented Cather's actual gender identity. Regardless, it certainly subverted the norms of the early twentieth century and could be a basis for the argument that Cather fits into a more radical type of feminism.
Keep in mind that this is just one way to define subsets of feminism. The feminist movement contains a wide range of viewpoints, and many individual feminists may identify in different ways.