Born in Baltimore, Maryland, Dobson was the second of four children born to Melvin and Evelyn Dobson (née Russell).[6] She attended Western High School, an academically demanding all-girls institution. Her father sold tickets for the Pennsylvania Railroad and her mother was a beautician. The family was poor, but Tamara had the full complement of piano, tap and ballet lessons. Her parents sent her on to the Baltimore Institute of Art, and after she got her degree, she went on to qualify as a beautician, like her mother.
Dobson experienced racial discrimination during her time working on films. When interviewed by The New York Times, Dobson said,
“I like being a woman,” she goes on. “I have the kind of job I want to do. I have been discriminated against, but not because I'm a woman. It's because I am black. I'm used to people not wanting to be with me because I'm black. Before they see me as being female, they see me as being black. The stigma that's been placed on you because you're black gives you enough kill to get you through the woman thing. It makes you angry! Yes, It's much tougher being black than being woman.” [8]