Plunkett's first diplomatic position was deputy consul in Honolulu, from 1974 to 1976.[3] She spent the next three years as third secretary of the Australian High Commission in Dar es Salaam.[3][1] She was also posted to Fiji (as First secretary), India, Tanzania and Hawaii.
Plunkett also held a number of positions in the Department of Foreign Affairs and Trade in Canberra. In 2005, as Director of Protocol in the department, Plunkett met with would-be Chinese defector Chen Yonglin to advise that the Australian Government expects resident foreign diplomats to return to their countries at the end of their postings.[4]
In January 2006, Plunkett was appointed Australian Ambassador to Ireland, with concurrent accreditation to the Holy See.[1][5][6] Her Holy See appointment was formalised by Pope Benedict XVI on 18 May 2006 when he accepted her letters of credence.[7][5] While Ambassador to the Holy See, Plunkett accepted a Papal rebuke over Australia's treatment of its Aboriginal people,[8] when the Pope called for ongoing attention to the social situation of Aboriginal people.[9] As ambassador in Ireland, during her frequent public appearances, Plunkett was noted for her ability to "pepper" ambassadorial speeches with "amusing anecdotes."[10][11]
In July 2008, the Australian Government elected to appoint a resident ambassador to the Holy See and Plunkett's role in the Vatican was handed on to another appointee. She continued as Ambassador to Ireland.[12]
From November 2009 to December 2011, Plunkett was Assistant Secretary, Protocol Branch and Chief of Protocol.[13]
In May 2012, Plunkett was appointed Australian Ambassador to Portugal,[14] with non-resident accreditation to Cape Verde and São Tomé and Príncipe.[15] She took up her appointment at the end of the year, and presented her credentials to the Portuguese Government in April 2013.[16] Her appointment in Portugal concluded on 19 April 2016.[17]