 Nyorai kupfuurira kweiyi ndima - Wheeldon akagadzwa kuva Gurukota reKudzorera uye Rudzikinuro muna June 1974 muhurumende yechitatu yaGough Whitlam uye akanga ane mutoro wokushandisa hurongwa hwaWhitlam hwekugadzira hurongwa hwekubhadhara nyika. Mukuwedzera, akagadzwa Gurukota reSocial Security muna June 1975 apo Bill Hayden akagadzwa Treasurer. Kugadzwa kwose kwakapedzwa nokudzingwa kwehurumende yeWhitlammuna November 1975. Wheeldon akaramba ari seneta kusvika musi wa 30 Chikumi 1981, asarudza kusapikisa sarudzo dza1980. 