Does the Governor-General vote in elections?
Great question, thanks John! As an Australian citizen over the age of 18, the Governor-General is required by law to be enrolled to vote.
By convention – tradition — the Governor-General does not vote as they represent the monarch. Before a federal election, the Governor-General or their Official Secretary writes to the Electoral Commissioner to confirm that the Governor-General won't vote. This is accepted by the Australian Electoral Commission and the Governor-General is exempt from having to vote.
Casting a vote for the House of Representatives.

Australian Electoral Commission
Description
A green ballot paper is put into a ballot box labelled 'House of Representatives/GREEN/Ballot Papers'.
Permission should be sought from the Australian Electoral Commission (AEC) for third-party or commercial uses of this image. To contact the AEC email: media@aec.gov.au or phone: 13 23 26.