Moller's first international competition was the 1974 British Commonwealth Games at Christchurch, where she finished fifth in the 800 m. Her time of 2:03.63 was her lifetime best and is still the fastest ever by a New Zealand junior (under 20) woman.

Moller was instead selected for both the 1500 m and 3000 m at the 1982 Commonwealth Games in Brisbane, winning bronze medals for both events.

As of June 2008[update], Moller ranked in the all-time top ten in New Zealand for the 1500 m, mile, 3000 m and 5000 m. She also ranked 11th for the 10,000 m. Personal Bests: Moller ran her first marathon on 23 June 1979, winning Grandma's Marathon in Duluth, Minnesota in 2:37:37.

Her full records are: She also won the silver medal at the 1986 Commonwealth Games in Edinburgh, running 2:28:17, her lifetime best.

[5] In the 1993 New Year Honours, Moller was appointed a Member of the Order of the British Empire, for services to athletics.