Namely gold in that case. A massive gold rush in Victoria in 1851 was the primary source of the gold. Trade (i.e. profiting from the manufacture of raw goods, taxes on production and materials, tariffs, etc) also allowed some level of revenue. The biggest source of tax money was in customs (import/export) and exise duties placed on the manufacturer (you had to pay taxes at harvest for the tobacco you had grown, for instance).

As far as how British North American colonies were intended to make money and started, I recently covered that here: https://www.reddit.com/r/AskHistorians/comments/gjj4kk/in_the_early_days_of_colonialism_in_north_america/

TLDR is they went for gold. They made a little money on trade, but the whole thing financially never paid itself off. Much of the investment money came from private citizens and not the crown itself.

As far as how Australia became independent, that's the Statute of Westminster, signed in 1931. It gave New Zealand and Canada independence as well. I speak more of the colonial empire downfall here: https://www.reddit.com/r/AskHistorians/comments/gbyzgn/honest_question_why_have_the_british_been_so_bad/

A point I'll add is that colonists were citizens of the colony and subjects of the crown. A citizen has authority. A subject is under the authority of another.

As previously mentioned there was the 1850s Australian Gold Rush, I'll just add that what allowed for that to happen was Australia transitioning out of penal colony regime in the VERY early years between 1788-1820. High ranking officials, emancipated convicts and other free people were able to acquire land grants to farm and mine.

Initially Australia's economic potential was not even realised as a penal colony, in fact the British Empire largely neglected Australia during it's initial years as they were fighting a war with the French. Noel George Butlin, an economic historian, refers to Australia's penal regime economic years as a 'bridgehead economy'.