Australian Politics: My Vague Understanding

So the other week (about a month ago) Australians Prime Minister was a man named Kevin Rudd, or more affectionately K-Rudd. Then magically he wasn't and instead the Prime Minister is now a woman named Julia Gillard. Was there an election? Was it the natural changing of leaders? Did he die? NO! Apparently the changing of Prime Ministers is not a difficult thing and can happen a couple of ways. First, and how it was done here, starts with the fact that Australians do not vote for an individual, but rather a political party. This means that if the political party does not like how the PM is doing their job, they can vote in a new PM, who I think asks for the job. If everyone agrees, or the current PM accepts defeat, then BOOM! new PM. That's what happened here, and it was super weird. The other way, which I think is amazing, is that, because Australia is a British Commonwealth, the Queen of England can decide that she doesn't like the Australian PM, will call up and say she doesn't like him/her and Australia HAS to get a new PM. Crazy, right? I love it, it's hilarious.
Elections are super weird here as well and tied to how long a PM has power, which is tricky. They are in control for 2-3 years at a time. 2-3 you ask? Why is it unknown? Well it's unknown because the PM gets to choose when the election happens after their first two years. This has it's advantages because you don't have to listen to election craziness for that long. Also everyone has to vote. If you don't vote you get fined. Which I think may be a good thing especially when right now the two people running for PM aren't that great and I think that no one wants to have to pick, so if people didn't have to vote they wouldn't.
Really the whole thing is quite strange, but definitely interesting to watch.