Note To Our Australian Friends: Don't Panic Mr Mainwaring!

So, it looks like a hung Parliament.  The first time for a long time for the Australian Federal Parliament.

But a quick note of advice to our Australian brethren.  Don't panic!

It's not actually unchartered territory.  While the constitutional history and context might differ slightly, you might consider glancing over to New Zealand to see the heavily developed and carefully framed constitutional conventions surrounding the appointment of the Prime Minister by the Governor-General in such situations.
One of the best guides is Sir Michael Hardie-Boys' 1997 Harkness Henry Lecture "Continuity and Change":

- http://www.gov-gen.govt.nz/node/471

Actually, there are a range of other speeches which also speak to the conventions surrounding appointment:

- http://www.gov-gen.govt.nz/resources/media/speeches/constitutional

If I can highlight the key passage:

The core principles
Through this public speaking and writing I tried, in essence, to make clear a few simple points:
- The formation of a government is a political decision and must be arrived at by politicians.
- My task as Governor-General is to ascertain where the support of the House lies. In an unclear situation, that might require me to communicate with the leaders of all of the parties represented in Parliament.
- Once political parties have reached an adequate accommodation, and a government is able to be formed or confirmed, the parties could be expected to make that clear by appropriate public announcements of their intentions. At that point it might be necessary for me to talk with some party leaders. I would then expect to have sufficient information to be able to appoint a new Prime Minister, if that were required.
- Throughout this period of negotiation, the incumbent Prime Minister remains in office, governing in accordance with the caretaker convention.
The second of these points is the nub of the matter. In a parliamentary democracy, the exercise of my powers must always be governed by the question of where the support of the House lies. It is this simple principle which provides the answer to those who sometimes suggest that in situations like that encountered by New Zealand after the last election, the head of state should simply call on the leader of the largest party to form a government. Size alone provides no reason to prefer a party if its leader does not appear to have the support of a majority of the House. It is better to wait for negotiation among the parties to produce a majority. This principle is also the answer to those who regularly write to Government House suggesting that the Governor-General dismiss the government and call another election, based on perceived public sentiment, dissatisfaction with particular actions, or opinion polls. To repeat: in a parliamentary democracy such as ours, the exercise of the powers of my office must always be governed by the question of where the support of the House lies. If that is unclear, I am dependent on the political parties represented in the House to clarify that support, through political discussion and accommodation.

And from a later speech (http://www.gov-gen.govt.nz/node/403):

Politicians may assist during a time of political uncertainty by indicating publicly where they stand in terms of their support for the Government. A vote of confidence is nonetheless the more critical indicator.

Good luck!