If im not mistaken, but I believe England, Wales and Scotland form a union that is the United Kingdom, they were seperate Nations first, unlike NSW and Queensland. (although, NSW is a matter of opinion).
Sort of. England has been lording it over Wales in one way or another since the 10th century and harassing them since much earlier. The current Welsh Assembley have much reduced powers compared to the Scotish equivilant.
Scotland and England formed a Union in 1701, but there is a great deal of history between the two. A lot of bribary and politics went into this, as well as forming based on the principle of mutual prosperity and security, the same basic idea behind any federation... eg UN, USA, EU and some elements of the British Empire (see Niall Fergusons book Empire... one of the best books I have ever read. I rate his TV show on Money too). Scotland was looking at having a referendum on breaking from the UK in 2010 or 11, but it got shot down. Still might happen in future.
If Scotland ends up a republic before Australia does is a national disgrace for Australia honestly.
And the final "home nation", Ireland, well we all know the history there.
Australia's history is completely of subserviant colonies bickering amoungst themselves for money and position, but never as nation states. Same reason why cohession on things today like a world cup or standardising education, hospital care, roads et cetera is very hard to get. The states love to fight each other.
Interestingly, WA almost didn't join Australia when federation occured because they thought they would be subjected to Eastern Australian dominance, but joined in the end when they saw the financial and security benefits. Seems that mentality hasn't gone away after 100 years.
Also, NZ almost did join in Federation, only to pull out at the last second. The original constitution document has New Zealand listed as one of the colonies to become states and Western Australia isn't.
There are three key areas of government that a nation has; head of state, parliment and justice system.
Australias head of state is still the queen, but the Governor General is the de facto ruler. The first Australian in the post was Issacs Issacs in the 30s forcing the British to apoint a commissioner to Australia in 1935, but after him there have been a long list of English or very English "Empire-men" right up to the last of them in Kerr in the 70s, who ironically by dismissing Whitlam also set the trend of G-Gs exercising the power of the Queen, making the monarch a rubber stamp. The prominence of Labor governments in the 1970-90s is what has set the trend towards truely Australian G-Gs who can exert the power of the monarch (thanks to Kerr).
As far as our judical system is concerned, it has only been completely independent of the British System since 1986. Another key date here is 1975 apeals act which almost made Australia fully independant in the courts.
Finally our Parliament has been independent, but has taken a long time to evolve into what it is today. Labor (but later conservative) PM Billy Hughes caused a lot of trouble during and after the first world war for the british empire (his protection of the White Australia policy at the Paris 1919 peace treaty was actually one of the catalists for nationalism and fascism in the 30s; easily Australias worst PM, but he was there for a long time (Just because a PM rules for a long time doesn't make them great)), but in terms of government functions, Australia was pretty much subservient to Britain until the second world war when John Curtain said that Australia has to look to America, China, Russia and others for our future and not just Britain. (This is where the idea of ANZUS starts).
He had to fight Churchill very hard to get Australian troops sent back to Australia from North Africa, (Churchill tried to have them sent to India when he couldn't keep them in Africa instead of going to PNG) and is historically seen as an important moment in the powers of Australian parliament. Then we had Menzies and other liberals until the 70s pretending it was still the world of Pax Britania and the cold war was raging, until the modern era of politics started with Whitlams reforms.
Australia has only truely been independent (with the Queen wearing the hat of "Queen of Australia" seperate from the British crown) from the mid 70s or 80s on all three areas of governance.
All that is left to do to be a republic is get rid of the Queen's title, and all the "in theory" power she has. I think a far more important thing for Australia though is constitutional reform... look at the way the state and federal governments work and try to structure it better. The current set up was good in 1901, but is looking terribly daggy in 2009.