Fullerton completed a PhD in human genetics at The University of Melbourne in 2001, and developed her career interest in psychiatric genomics over the next five years as a postdoctoral researcher at The Wellcome Trust Centre for Human Genetics (University of Oxford, UK). She returned to Australia on a 2-year NHMRC Howard Florey Fellowship based in Sydney, split between The Garvan Institute for Medical Research and The Prince of Wales Medical Research Institute, now known as Neuroscience Research Australia (NeuRA). Between 2013 and 2025, Fullerton led a multidisciplinary team at NeuRA focused principally on bipolar disorder, as well as related clinical symptoms and diagnoses including schizophrenia, psychosis, suidical behaviours and substance use. 

Fullerton is a contributing member of a number of international consortia including The Psychiatric Genomics Consortium, Consortium for Lithium Genomics, Enhancing Neuroimaging Genomics through Meta-Analysis (ENIGMA), a Bipolar High Risk Consortium. Fullerton has served on the Advisory Committee for the NIH-funded International Bipolar Sequencing Consortium, the Asia-Pacific Steering Committee of the Global Bipolar Cohort Collaborative, and the Research and Clinical Advisory Committee of the Mindgardens Neuroscience Network.