There are no special rules for visitors wanting to detect in Australia, as a visitor you have the same rights as me.
Detecting for coins and artifacts does not require a permit but in some states you are required to hold a Miner's Right for detecting for Gold.
In Western Australia a Miner's Right costs $25, our dollar is on a parity with the $US dollar at present. This Miners' Right is a once off lifetime licence and available from any W.A. mines registrar.
In Victoria a Miner's Right is $29.90 for 2 years.
In Queensland you must have a Fossicker's Licence this costs $6.50 for one month or $24.20 for 6 months.
There are laws when detecting for Gold, such as areas covered by mining leases, exploration leases etc. where you need permission of the lease holder, most of this information is on-line, Google the Department of Mines in State you want to visit
No licence is required for South Australia, Northern Territory or New South Wales provided you abide by a few simple rules and are not a professional.
While there is no licence for coin hunting or relic hunting common sense prevails, don't dig up parks etc. It is however illegal to detect in National Parks.
I hope this helps, if you want further info don't be afraid to ask.
Regards, Brian