Morgan is the director at the Centre for Indigenous History and the Arts at the University of Western Australia. She has received several awards: "My Place" won the Human Rights and Equal Opportunity Commission humanitarian award in 1987, the Western Australia Week literary award for non-fiction in 1988, and the 1990 Order of Australia Book Prize. 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.