You are comparing an island with low-density population with huge continents, one of them with poorly enforced border control. The amount of confounding here makes it impossible to attribute Australia's success to its policies.
Australia quarantines internally, which is comparable, if not more difficult, than countries that close their international borders. Imagine if LA was quarantined from the rest of California. That's the closest analogy I can make to the subject of this thread.
And yes Australia is a large island but if you take the briefest glance at a population density map, you'll see that the vast majority of the population is concentrated in a few coastal regions and particularly around Sydney and Melbourne.
Lockdowns are not 100% effective, but just an attempt to slow down the transmission rate. Think of it as a type of defense-in-depth. Australia (and New Zealand's) true advantage is their natural isolation from the rest of the world and their ability to control/track who is coming into the country.
Arguably the US would have it easier to control, since half its population is in low density rural and suburban environments that significantly reduce social contact.