Dorothy Dusty Baxter Alexander was educated at the McGill University Architectural School in Montreal. She started work for the architect, John Carl Warnecke in February, 1955. She later worked for the firm Wurster, Bernardi, and Emmons before starting her own firm in April of 1961. Her architectural credits include commercial remodelling for the Arriflex Corporation, Lowel-Light Manufacturing, Panavision and the Jack Tilton Gallery. She has also done restoration work on housing, as well as, designed houses and duplexes in the San Francisco area.

Alexander also works as a photographer. In 1981, Alexander became a staff photographer for Skyline, the magazine for the Institute for Architecture and Urban Studies. During the 1980s through the early 1990s, she worked as a photographer for The Writer's Voice, The Academy of American Poets, West Side Spirit, and the Toronto Globe & Mail. Since the late 1980s Alexander worked as a photographer for Oculus, the magazine for the New York Chapter of the American Institute of Architects.

Alexander's photographs have been the subjects of numerous exhibitions in New York. They focus on urban landscapes, street portraits, and some abstract work. Her work is in the main collections at the Bibliotheque Nationale de Paris and the National Portrait Gallery in Washington, DC.