Dawson is the great-granddaughter of the astronomer Bernhard Dawson and the granddaughter of the geologist Mario E. Teruggi. Dawson had four children. Of these, Diana Teruggi de Mariani (December 3, 1950, La Plata - November 24, 1976) was executed by military forces, and Diana's baby, Clara Anahí Mariani (born August 12, 1976, La Plata), was kidnapped and deprived of her identity.