Her mother, a member of the Bailgu people of the Pilbara region of Western Australia, grew up in the Parkerville Children's Home as part of the Stolen Generations.
[1][10] As a child, Morgan became aware that she was different from other children at her school because of her non-white physical appearance, and was frequently questioned by other students about her family background.
[1][5] The story of her discovery of her family's past is told in the 1987 multiple biographies My Place, which sold over half a million copies in Australia.
In 1993, international art historians selected Morgan's print Outback, as one of 30 paintings and sculptures for reproduction on a stamp, celebrating the Universal Declaration of Human Rights.
In 2023 The West Australian newspaper identified the 100 people who had shaped the state of Western Australia and they included senator Jo Vallentine, politician and businessperson Carmen Lawrence, health activist Fiona Stanley, politician Bessie Rischbieth, Dr Roberta Jull, women's leader Amy Jane Best and Morgan.