Australia's top exports are also based on natural resources, namely, Iron Ore, Coal Briquettes, Gold and Petroleum Gas, accounting for 60% of all exports at $144.6B. Assuming a population of 24.6M, this translates to $5.9k per person.
Point is, while Australia isn't quite as well off as Norway, there are resources aplenty to pull off something similar on a somewhat smaller scale.
Metals is an interesting case because on the one hand they are definitely a non-renewable resource. On the other hand, it seems like there's a difference between exporting ore and exporting refined metals, in terms of whether it's "just" resource extraction or not...
Iron ore extraction isn't bad but it's nowhere near as profitable as Norway's oil extraction
You'd have to do that across the entire range of resources and then divide per capita - on that basis I think Norway would blow by 4x Australia just based on off-the-top of my head estimate