Australia is big. Really big. It's about the same size as the continental United States. I'm saying this because it often comes as a shock to visitors, who seem to expect to merrily drive from one destination to another. You can't. I don't care what it looks like on the map.
Not only are attractions in Australia generally quite far apart, but because the country's population is actually fairly small*, long distance transportation here just isn't as accessible as it is in the States. There aren't as many plane flights available, and they're often several hours long, although that's still preferable over bus or train trips, which can take days (I once took a bus from Sydney to Alice Springs and spent 48 hours on board - NOT fun). To get from one attraction to another, you will generally have to fly to the nearest major city, then take a bus/train/car to your ultimate destination, so you can spend a great deal of your vacation time in transit if you're not careful with your planning.
If you want to see the entire country, I strongly recommend allowing not less than four weeks. If you have three weeks, you can see some of the east coast and the Red Centre (you'll probably want to go there since that's where one of Australia's biggest attractions is located). If you only have two weeks, I'd stick to the east coast only, visiting Sydney, Melbourne and the Great Barrier Reef. Any less than two weeks and I would choose a different destination, since you won't be able to spend much time outside of the city - and Australia's stunning natural beauty is by far it's biggest draw card.
* The national population was a bit over 21 million at last count. To put that in perspective, New York City alone has just under 9 million people. The population of the continental United States - which, keep in mind, is roughly the same size as Australia - is just over 303.5 million. England has over 51 million people and is only 1/59th the size of Oz (no that's not a typo: Australia's landmass is over 59 times greater than England's).
This made more sense when I was unconscious. - Last night I dreamt this really profound statement which I suspected I’d forget if I didn’t write it down, so I jotted it down quickly and fell immediately...