The Academy of American Poets, Inc. wrote that young Dorothy Parker attended a Catholic grammar school called Blessed Sacrament Academy, a finishing school known as Miss Dana's in Morristown, New Jersey, and the Art Student's League in Manhattan. Although she never received a high school diploma she continued to read and use her life experiences to fortify her own education.
She became a great poet because of her harsh and sad up bringing. She lost her mother when she was five and grew up quite distant from her father and stepmother. She endured personal pain and sought out her own identity. She understood the stereotypical roles of women and despised them. She rebelled against her distant father and stepmother and eventually rebelled against many common notions of proper society.
I believe your answer about Dorothy Parker's education lies less with her formal educational background and more with her life experiences.