Born in Ross Street, the youngest of five, her parents were Alexander Rae, a cutler, and his wife Mary. Noyce had a daughter Violet (b. 1923), and took the surname of her child's official father to use as a pseudonym. Noyce had begun to operate as a madam from premises at 17 Danube Street, Stockbridge, Edinburgh by the end of the war and remained there until her death. She owned other properties in the city and in Blackpool.
Overseeing 15 resident prostitutes, Noyce was able to draw on up to 25 other women in busy periods. Her employees apparently had regular health checks. Queues formed around the block when certain ships were in port. When the aircraft carrier USS John F. Kennedy was in dock at Leith, the women reportedly did £4,000 of business in one night and the ship's captain declared the house off-limits. Noyce was charged 47 times for living off immoral earnings, generally paid the fine instantly, and served a four-month prison sentence in 1972, her last period in custody. Local councillors commented that they received more complaints when Noyce was in prison because her business was less well managed.
While she claimed in an interview that demand for her services was greatest during the Edinburgh Festival, her second busiest period was when the general assembly of the Church of Scotland was in session. A Conservative supporter who had banners for the party in her windows at election time, she embarrassed her member of parliament by turning up at garden fetes.
Dora Noyce became one of Edinburgh's characters, well-known to locals, who was mourned when she died. A correspondent to The Scotsman newspaper wrote: "I confess to having felt something of affection for Dora Noyce. At least she was prepared to accept responsibility for what occurred within and outside of her premises. ...It may well be that Mrs Noyce was right when she always claimed that she offered a necessary social service."
- Sandra Dick "Danube Street brothel: From sex-starved sailors to the Capital's establishment", Edinburgh Evening News, 25 February 2009
- Katie Emslie "Nights at city's blue Danube St", Edinburgh Evemning News, 14 December 2005
- Brian Groom "Notebook: Virtues and vices of the manse", Financial Times, 3 September 2007
- Brian Meek "Prostitution and the least awful option ", The Herald (Glasgow), 16 September 2003
- Letter to The Scotsman, 26 August 1977, quoted by Liz Bondi "Sexing the City" in Ruth Fincher and Jane M. Jacobs Cities of Difference, New York: Guilford Press, 1998, p.194-95