I'm also in Australia and yes, it is the skin cancer capital of the world.
If I walk around the Gold Coast (lots of beaches) I would tend to see quite a few people fitting the original description. Sun bronzed leathery wrinkly skin. It looks horrible.
So...wear sunscreen as high protection as you can get. In Australia sunscreen manufactuers are not allowed to advertise protection over 30+ for any sunscreen so comparing different 30+ brands is quite difficult. However, the active ingredient Titanium Oxide is more effective than Zinc Oxide so try and find something with this or so my doctor says.
I have had the experience of sitting into some seminars done by some sun damage and cancer related researchers. They have come back with the result that you don't have to be visibly burnt to increase your risk of cancer. The speaker said that 15 mins unprotected sun at the time (the seminar was in mid Spring) would be plenty of time to cause damage that leads to skin cancer. Granted this is Australia whcih would get more sun that other parts of the world but the message is clear that it doesn't take much and you don't have to get burnt regularly to be at high risk.
So, being naturally pasty white (or bright red when I miss patches and get burnt) with freckles and blue eyes I slather myself with the 30+.