Rosemary Dobson's father (son of English poet Austin Dobson) died when Dobson was five and her older sister Ruth seven years old, leaving her mother, Marjorie Dobson, to raise her daughters in straitened circumstances. Dobson was educated at Frensham school (Mittagong, N. S. W.), where she published her juvenile Poems (1937), producing its linocut cover in addition to printing and binding the volume.
After a brief period teaching art at the school, Dobson studied English literature at the University of Sydney as a non-degree student, and studied drawing with Thea Proctor, one of Australia's best known artists. In her early twenties, she commenced employment with publishers Angus and Robertson, where she worked with Beatrice Davis, an influential nurturer and editor of Australian literature during the immediate post-war period. During the 1940s, Dobson established friendships and working relationships with many of Australia's most significant writers, including Douglas Stewart, Norman Lindsay, Francis Webb and Nan McDonald. Dobson met Alec BoltonaP) in 1950 when he joined Angus and Robertson as an editor, and they married the following year. Their three children, Lissant, Robert and Ian, were born during the 1950s, while the family lived in Sydney. Bolton was appointed Angus and Robertson's London editor in 1966, and the family enjoyed a five year sojourn in England, during which Dobson and Bolton developed their interests in European art, music and literature, and in fine printing.
The family returned to Australia, moving to Canberra in 1971, when Bolton was appointed the first Director of Publications at the National Library of Australia. Although Dobson undertook some tutoring and editing whilst raising their family in the 50s, 60s and 70s, her main non-family work was always her own poetry, which flourished in the rich literary atmosphere of Canberra. Important literary friendships were forged during this time - especially those with poets David Campbell and James McAuley. Bolton's passionate commitment to small press work, his establishment of the Brindabella Press in 1972, and his eventual retirement from his National Library position in 1987 to work with the Press full time, deepened the couple's ties with Australian literary production, and their relationships with the select handful of Australian writers whose works were published by the Press, including David Campbell, R. F. Brissenden, A. D. Hope, James McAuley and Philip Hodgins.
Dobson provided editorial advice and proofreading services, and produced illustrations for several of her own works produced by the Press. Dobson remained in Canberra after Bolton's death in 1996, and published Untold Lives and Other Poems after her eightieth birthday. Dobson's contribution to Australian literature has been recognised through numerous awards and an Honorary Doctor of Letters from the University of Sydney. In 2000, the National Library of Australia held a 'Celebrations' for Rosemary Dobson (as they had previously done for Alec Bolton, in 1993), and published an accompanying tribute volume, Rosemary Dobson: A Celebration.
A celebration for Dobson's 90th birthday was held at the Australian National University Arts Centre, 8 June, 2010.