Thanks for your question. In short – yes they can!
The Prime Minister is the leader of the Australian Government and the leader of the nation. By convention (tradition), the Prime Minister is a member of the House of Representatives who leads the parliamentary party, or coalition of parties, with the support of the majority of members in the House.
To qualify to be elected as a member of the House of Representatives candidates must be Australian citizens and be eligible to vote. Senators, members of state parliaments, public servants, including defence personnel, and officers of the Electoral Commission are not eligible to become members of the House of Representatives and must resign their position if they wish to nominate for election to the House. People who are citizens of, or hold allegiance to, a foreign country; who are undischarged bankrupts or who have been convicted of certain offences are also not eligible to become members.
Candidates for election to the House must be nominated by a political party or by at least 100 electors of the electorate to be contested; however, a sitting member who was elected as an independent needs nomination by only one elector if he or she wishes to stand again for the same seat. On nomination candidates pay a deposit of $1000. This is returned if the candidate is elected or receives at least four per cent of the (first preference) votes cast in the electorate.