Specht worked as a senior research fellow at the University of Adelaide from 1950 while he worked on his MSc. He was appointed a lecturer in botany in 1951, and worked on his PhD for the next two years, on mineral nutrition and biomass relationships of the heath vegetation at Dark Island, South Australia. He rose to Senior Lecturer in 1955. In 1956, Specht earnt Fulbright, Smith Mundt and Carnegie grants to study in the U.S.