When you get married, you are expected to leave your job and rely on your husband, at the time, so most women working would be young or too old to get married. At home, women did handcrafts to bring in money such as quilting and also washing and other chores.
In 1921, just coming out of the war, some women were reluctant to give up "men's jobs" but they were more or less forced out of most industries thanks to the American Federation of Labor. One place they were pushed to stay was in textile mill/garment factory work.
There was demand for a growing secretarial/clerical workforce: typists, filing clerks, stenographers. Hotel workers. In department stores there was real potential for women to work up to becoming designers or buyers. There were more women journalists, women creating & writing literary journals, women's magazines. Entertainers, dancing, acting (stage and radio and film), and singing.
A really cool female character would be a professional medium, someone who bilks people by pretending to talk to the dead. Men did it too, but women were the most successful and popular mediums.