It's a little more complex: it's a pure parliamentary system, so, in a vacuum, you vote for your constituency's member of parliament running against other candidates (simple majority). These then go to parliament where they will form a government and select the prime minister. If there were no parties and they elected all independents they would bicker for weeks. With parties, the leader of the party with a majority (first past the post) of MPs simplifies the process and just becomes PM.

In other words, imagine just voting for House of Reps, the one with most seats gets to go to government, and the senate is actually an unelected coterie of nonces selected by just some guy, in some cases for life, in some cases hereditary, in some cases both.

Other countries have a system like this, so it's not too unusual