Guðrún first worked as a secretary at a school in Reykjavík, and then as department manager at the National Health and Insurance Office. She was a city councillor for the People's Alliance from 1978 to 1982, and a member of the Icelandic legislative assembly from 1979 until 1995. In 1988 she became Speaker of the Alþing, the first woman to hold the position. She is one of the best known children's authors in Iceland, and in 1992 received the Nordic Children's Book Prize for Undan illgresinu (From Beneath the Weeds).
