Garson won a Royal Society postdoctoral fellowship after her PhD, undertaking research in Rome, Italy from 1977 to 1978. She continued her research at New Hall at Cambridge on a college research fellowship from 1978 to 1981. She worked as a medicinal chemist from 1981 to 1983 at Smith Kline and French Research Ltd in Welwyn, England,.
Garson won a Queen Elizabeth II Research Fellowship from James Cook University (1983–1986), based in the Townsville region to research the bioactive organic chemicals in marine organisms. In Townsville, she undertook dive training to study on the Great Barrier Reef. Garson then took a teaching/research position as the first female academic in chemistry at the University of Wollongong, before moving to the University of Queensland as a lecturer in 1990. She was promoted to Senior Lecturer in 1992 and Reader in 1998. She researches and publishes on the structure, biosynthesis and function of natural products, especially those from marine invertebrates and other microorganisms. She also researches the chemistry of South East Asian medicinal plants.
Garson was promoted to Professor in the School of Chemistry and Molecular Biosciences in 2006, and has served as Deputy Head of the School from 2005 to 2009. Since 2021, she is an Emeritus Professor of Chemistry at the university.