Deepani obtained her MBBS with honours from the University of Peradeniya, Sri Lanka in 2001 and was awarded the Barr Kumar Kulasinghe memorial prize for surgery. In 2009 she obtained her MD in dermatology from the Post Graduate Institute of Medicine -University of Colombo and while training for the MD she worked at The National Hospital of Sri Lanka, the Lady Ridgeway Childrens Hospital, Colombo and the Colombo South Teaching Hospital.
She worked as a Dermatology Fellow at the St. Vincents Hospital, Melbourne from June 2009 to July 2010. She was the recipient of the Sixth Dr. D. A. Gunawardana Memorial Gold Medal awarded by the Sri Lanka College of Dermatologists in 2010.
As a Consultant Dermatologist she practiced in public and private hospitals in Sri Lanka for four years before joining the Sinclair Dermatology, Melbourne in June 2014. In February 2015 she became a Fellow of the Australian College of Dermatologists.