During her career Möller always stood in the shadows of Göhr, Marita Koch, and Heike Drechsler. Only in 1987, while still using her maiden name Gladisch, did she come into her own: at the track and field world championship of 1987 she won two titles – in the 100 m sprint and the 200 m sprint, as well as second place with the 4 x 100 m relay team. With these results she was chosen as the East German sportswoman of the year.
Möller's 200m final performance at Rome in 1987 was exceptionally fast, she stopped the clock at 21.74 seconds. She had won the race by several meters and defeated a world class field including Florence Griffith and Merlene Ottey. Her time of 21.74 seconds was only just outside the then world record of 21.71 held by Marita Koch and Heile Drechsler.
In 1992 she was implicated with Katrin Krabbe and Grit Breuer in a doping scandal, but would later be cleared by the International Athletic Federation (IAAF). Shortly before the 1992 Summer Olympics she quit her athletic career and began to study history in Rostock. She worked as a history and sports teacher. She has a daughter (Kristin).
Möller represented the Empor Rostock sport club and trained under Wolfgang Meier (Marita Koch's coach and now Husband). While she was actively competing, she was 1.63 metres tall and weighed 57 kilograms.