Internationally, the importance of science, technology, engineering and mathematics (STEM) for innovation and competition drives concerns about the adequacy of national STEM workforces. Data from the UK, USA and Australia suggest that, even immediately post-graduation, a significant proportion of engineering bachelor graduates do not work in engineering roles. Using the 2011 Australian census data, we present an investigation into the relationship between educational qualifications and occupational status of Australian engineering bachelor graduates, and how this status varies specifically with graduate age. We consider the implications of these findings and present recommendations for the recruitment and education of Australian engineering undergraduates. We conclude that engineering students would be better informed about, and equipped for, the world of post-graduation work if they were exposed to the likely options for their career trajectory. Likewise, secondary school students and others considering engineering undergraduate study would be more honestly advised if they were informed about the full range of career possibilities for engineering graduates and the probability that they are just as likely to work out of engineering as in it.