Henderson attended the Cologne Musikhochschule, where she studied with Mauricio Kagel and Karlheinz Stockhausen. Receiving a scholarship from the German government in August 1974 she attended the Darmstadt Summer Courses for Composition and Performance. The short music-theatre piece Clearing the Air was written during the two-week period in Darmstadt, and with it Henderson won First Prize for Composition at the course's end. At the end of a year's study with Kagel, Henderson produced a concert of three of her works at the Musikhochschule, as a result of which she was commissioned by the Braunschweig Opera Studio to write Mutti Kirche (Mummy Church).

Henderson returned to Australia at the end of 1976 and settled in Sydney. She was awarded a part-time Fellowship by the Australia Council and worked on her first two Australian commissions, Alanbiq, commissioned by Musica Viva for the Percussions of Strasbourg's 1978 tour of Australia and New Zealand, and Split Seconds, a music play for radio, for the ABC. Split Seconds was awarded an honourable mention in the Drama section of the Italia Prize in 1978.

Henderson taught composition as a part-time lecturer at the University of Sydney in 1976. She became resident composer in the Department of Music there in 1978 and, over the three-year span of her appointment, worked to stimulate the interest of students in music-theatre, and to encourage them to create their own music-theatre compositions.

In September 1983 Henderson's work for organ and pre-recorded tape, Sacred Site, was given its first performance in the Concert Hall of the Sydney Opera House by David Kinsela. This work was commissioned by the Sydney Opera House Trust to celebrate the tenth anniversary of the opening of the Opera House, and Henderson believes that it holds a seminal place in her compositional output.

Moya Henderson's work as a composer has also led her into the field of instrument design. While in Germany in the mid-seventies she received a commission from the sculptor Helfried Hagenberg to compose music to be played on a sculpture he had created from twenty-seven triangles. The sound she discovered during the course of completing this commission led her to research and eventually develop the alemba, a keyboard percussion instrument. The first prototype of this instrument was created in 1983, with the assistance of grants from the Federal Department of Science and Technology, the A.S. White Trust and the Myer Foundation. She was awarded one of the inaugural CSIRO Artist-in-Residence Fellowships in November 1983, and another residency in 1986 enabled her to work on an improved fine-tuning of the bass alemba. Treble and bass alembas have been used several times by the Sydney Symphony Orchestra, and Henderson has continued to work to perfect the instrument's design.

Henderson is also the inventor of the Tosca Bells, another instrument created with the assistance of the CSIRO. She also developed the 'noose' for stringed instruments, which enables the composer to write 'natural' harmonics on virtually every note within the range of the string orchestra. The first work to make use of this invention was Henderson's The Dreaming, composed to a commission from Musica Viva for the Australian Chamber Orchestra.

Moya Henderson has received many commissions from a variety of organisations, performers and ensembles such as the Australian Opera (her opera, Lindy, based on the Azaria Chamberlain case), the ABC, Musica Viva, West German Radio, Macquarie University, Helen Noonan, David Kinsela, the Australian Youth Orchestra, and Perihelion. In 1989 she was the recipient of one of four inaugural Composer Fellowships awarded by the Performing Arts Board of the Australia Council. She was awarded the Don Banks Fellowship for 1993 and was appointed Macgeorge Fellow with the University of Melbourne's Music Department for the first quarter of 1995.