Australian anti-republic arguments

The Monarchist has a post on the strategies the monarchists intend to "explain" to the Australian public:

A president would mean yet another level of government with a separate mandate to the government of the day.

This depends on the model of republic the Australian people choose. A ceremonial president - such Ireland has - does not mean "yet another level of government", a non-executive office would not require advisors and technocrats as a executive office would. The mandate issue is a vexed one - the claim is that a elected head of state leads to instability. That's not the case in countries like Ireland, Austria or Iceland, all of which are mature democracies like Australia and New Zealand.

The Queen’s only role in Australia is to appoint the Governor-General on the advice of our Prime Minister (and State Governors on the advice of the State Premiers).

Well, this only shows the Queen's position is pointless.

The Australian Governor-General is Australia’s Head of State – This was stated by the Australian High Court as far back as 1907!

No, the Australian High Court stated the Governor-General was the "constitutional head of State" - in other words, he or she carry out all of the functions of the head of State, the Queen. As Bryan at OzPolitics notes, the argument that the Governor-General is Australia's head of state is just a cynical attempt to manipulate the debate.

Because the Queen succeeds to the thrown by accident of birth she is above party politics, and because our Governor-General is also a representative of the Sovereign he/she is also above party politics.

The Queen doesn't simply become Queen by accident of birth. The Queen gets her position by being born into the right family, having no other male siblings, and staying in the Church of England.

Secondly, the Queen might be "above" party politics, insofar as Her Majesty doesn't get involved in her Commonwealth realms, but the Governor-General certainly isn't. Former Governors-General of Australia, as in New Zealand, are almost always linked to the political party in power. The next Governor-General of Australia, for example, has overt links to the ALP. Governors-General certainly aren't immune from political controversies.

To establish a republic would coast many millions of dollars, money that could be spent else where.

The alleged cost of a republic could of course be spent elsewhere. So could the defence budget or the electoral commission's budget.

The Crown is an institution that we share with many countries, not just the United Kingdom

This isn't really relevant to anything, unless you see the link to the United Kingdom and the other Commonwealth realms as something more than a personal union. It's not really - most of the links we associate with the monarchy are actually links through the Commonwealth, which has more republics as members than monarchies.

We have already had a vote on a republic in 1999

Everyone knows the 1999 republic referendum was rejected because of the expectation of a follow up referendum.