I think parent is referring to Engineers Australia (formally, the Institution of Engineers, Australia), which is the professional body to which most engineery-engineers belong.

Most "Bachelor of Software Engineering" degrees offered by Australian universities are EA-accredited and contain mandatory engineering courses that EA requires. Most CS/IT degrees that don't have "Engineering" in the degree name are only accredited by the ACS (or potentially not accredited at all).

I'm also an Australian software "engineer", I don't have an EA-accredited degree, and the more I see of this industry, the less certain I am that we get to claim the mantle of "engineer" with the professional responsibilities that go with it.