Can a Minister remain in their role while not a member of parliament? Section 64 of the constitution seems to imply they can for three months.

Commonwealth of Australia Constitution Act, 1900: Original Public Record Copy (1900).
Parliament House Art Collection, Art Services Parliament House
You are right John. Section 64 of the Australian Constitution gives ministers 3 months to gain a seat in either the Senate or the House of Representatives before they have to give up their job.
When a seat in the House of Representatives is made vacant, it is filled by a special election for only that seat called a by-election. Section 64 allows a minister to continue with their job while they are standing in a by-election.
The situation is different for senators. In 2017 a senator who was also a minister was found by the High Court of Australia to have been invalidly – not properly – elected. After she was removed from Parliament, the minister resigned her ministerial commission. Because there are no by-elections for the Senate, if the former minister wished to return to the Senate, she would have to stand at the next Senate election.