She completed a pediatric internship and residency at Babies Hospital and a fellowship in neonatology at Emory University School of Medicine.
[2] After her fellowship, Stoll was an associate scientist at the International Centre for Diarrhoeal Disease Research, Bangladesh.
She was a visiting scientist at University of Gothenburg where she researched systemic and mucosal immune response to diarrheal agents.
In 1984, Stoll became an assistant professor in the Uniformed Services University of the Health Sciences Department of Medicine.
She took a year sabbatical working for the World Health Organization where she raised awareness on neonatal morbidity and mortality in developing countries.
[1] As of 2015[update], she is the H. Wayne Hightower Distinguished Professor in the Medical Sciences, Professor of Pediatrics and former Dean at the University of Texas Health Science Center at Houston.