The information sources employed in classic genealogical practice and relevant to the period post-1960 are not available to you (because of restrictions imposed on privacy grounds) .
In cases such as this, it may be helpful to think about what other type of expertise could be relevant to locating a person who has "disappeared".
Perhaps you need to think like a debt collector or someone arranging a class reunion.
Have you considered Electoral Rolls, Phone Books and newspaper libraries as sources? Can you locate a social media guru who will help you to mine Twitter archives or Facebook posts?
As a worst case scenario, have you looked into lists of missing persons maintained by the police?
And something I should have thought of before
All Queensland State Schools keep an Admissions Register of details of every pupil enrolled. Microfilm copies in the Queensland State Archives contain name, date of birth, religion, and the name, address and occupation of parents. While there is no "official" index for these records, the Queensland Family History Society has produced a 5 CD set that enables you to match a name and approximate age to possible school enrolments. At least one of the subscription sites (fmp) searches on that QFHS derivative.
When (if) you identify some possible schools, you can check the availability of relevant registers online but after that is necessary to view the undigitised films in the old way.