Mr. and Mrs. Robert F. Cooke of allenhurst, N.J. have announced the engagement of their daughter, Deirdre Elizabeth to Donald J. Schroeder, son of Mrs. Kathleen Schroeder of Bloomfield, N.J.

Miss Cooke, who is studying voice, is an alumna of Marymount Secondary School, Tarrytown, N.Y. and the Marymount College of Virginia where she recevied her bachelor's degree. She made here debut in 1975 at a dinner-dance given by their parents for her and her twin sister, Eileen, at the Deal Golf and Country Club, Deal, N.J. She was a member of the St. Vincent dances in Westchester and the Gothmans in New York City. Her father is an investment manager. She is the granddaugher of Mrs. Thomas R. Brown of New York City and the late Mr. Brown. He was an executive of the State and Treasury Departments, the State Department's chief of security for the founding conference of the United Nations in San Franciso, and was also one of the original members of the office of security when the Central Intelligence Agency was formed. She is also the granddaughter of the late Mr. and Mrs. Edward F. Cooke. Mr. cooke was an investment manager.

Mr. Schroeder, an alumnus of Delbarton School, Morristown, N.J., also was graduated from Boston College. He is a financial analyst for Warner Lambert Company and is studying for his master's degree at Fairleigh Dickinson University.