Dunn was Senator for New South Wales first representing the Nuclear Disarmament Party (NDP), then as an independent. She became a Senator—notably, the first with Asian ancestry —in unusual circumstances, when Robert Wood was disqualified under section 44 of the constitution from holding the seat he had won in the 1987 general election. The High Court of Australia sitting as the Court of Disputed Returns found that a recount of the NSW Senate ballots could occur and Dunn, who had been the second person on the NDP's New South Wales Senate ticket, was elected. The NDP asked her to resign her seat to allow Wood to take it up once he had taken up Australian citizenship, but Dunn refused, leading to her expulsion from the NDP, after which she sat in parliament as an independent. She was a Senator from 21 July 1988 until 30 June 1990, being defeated in the 1990 election. During her time in office Dunn was active on one of the Australian Senate committees: Foreign Affairs, Defence and Trade. She was responsible for an extensive minority report to that committee's report "Visits to Australia by Nuclear Powered or Armed Vessels".