In Katherine Mansfield's story "The Doll's House", the characters are divided into two groups: those who are innocent to social class and status, and those who are not. Since the prevalent theme in the story is precisely that of social mistreatment against those who are indigent, you would have to separate protagonists and antagonists using that formula.
This being said, the protagonists are the Kelvey girls, Lil and Else. Lil, the elder sister, is described as a “stout, plain child, with big freckles". Her younger sister Else is insecure and follows Lil around, tugging at her. These girls are the daughters of a washerwoman who dresses them up in "hand-me-downs" that she gets from her patrons. There is no known father for the Kelveys...
But where was Mr. Kelvey? Nobody knew for certain. But everybody said he was in prison. So they were the daughters of a washerwoman and a gaolbird.
The reason why they are the protagonists is because they are the characters most affected, changed, or influenced by the central theme of the story. Out of the two sisters, the most changed is Else, who is the character that feels most transformed as she says the words:
I seen the lamp.
These words are important because they denote that there must have been an anxiety in this character to see the lamp and, after seeing it, something within her felt triumphant; likely, the fact that she had the right to see something unique, special, and which only those who have everything get a chance to witness.
The antagonist of the story is Aunt Beryl, although she represents a much bigger theme, which is social injustice. Aunt Beryl, who is characterized as a bitter, classist, mean, and secretive woman, is the blocking agent that prevents the girls from coming close to the doll's house. She represents the society of the "haves", and how they oppress and blow the spirit off the "have nots", treating the Kelveys badly and characterizing them as nothing short of vermin.
Keep in mind that, when the story was published in 1922, Katherine modeled the characters of Lil and Else Kelvey after a real family whom she knew about: the family of the local washerwoman's daughters, Lil and Else McKelvey. This is further evidence that she focalized the central theme of the story through the eyes of the poor girls more so than the Brunell's. Katherine Mansfield, who was from an affluent family, modeled Kezia after herself.
More on Katherine Mansfield in the links provided.