Quach was educated in New South Wales, where she studied under noted Russian conductor Nikolai Malko.

She then took a conducting course from Sir John Barbirolli and Carlo Zecchi in Italy before moving to the US to serve as an assistant to Leonard Bernstein.

[citation needed] Quach was born in Saigon on 4 July 1940, to Chinese parents; her father was in business and her mother was a musician.

"[6] In 1958, Quach was a second-year student at the NSW Conservatorium when she became one of the first two women awarded a scholarship to study under noted conductor Nikolai Malko, who was then the musical director of the Sydney Symphony Orchestra.

The announcements of the award had specifically excluded women, but Malko said he reconsidered because Quach and the other female recipient were "more than usually talented".

[4] In 1964, Quach won a scholarship for a conducting course taught by Sir John Barbirolli and Carlo Zecchi in Sicily.

[7] "Miss Quach runs the danger of being a pretty young woman, and thus conquering all hearts for non-musical reasons.

But ... she seems to be at her best in works of large dimension (odd for so diminutive a creature) and if there can be such a thing as a maestra, Miss Quach could well be it," Bernstein said.

[5] As an early-career conductor, Quach also spent three- to four-year stints in Paris, Hong Kong and Taiwan.

[8] In 1977, about a decade into her career, Quach was one of very few females conducting major symphonies anywhere in the world (others included Sarah Caldwell of Boston, Sylvia Caduff, and Zheng Xiaoying).