It depends is the answer, on many things.
Who owns the land.
These days out west here - one or another govt dept owns all of it - there's little "crown owned, common land" left.
They did this deliberately after the Mabo Decision to try and stop land rights claims over most of WA, all the crown land got vested as used for some purpose.
I know if a spot I believe there to be 3 barrels of Dutch Silver coins - brought to shore by Dutch Survivors off the Vergulde Draeke shipwreck.
Trouble is - while it isn't technically covered by the legislation of the shipwrecks act because it becomes a land treasure once the original owners brought it ashore and buried it - that wouldn't STOP our maritime Museum from claiming it under their act - they would find a way - calling it "other significant items" or some such as listed in our agreement in the Hague in 1972 with the Dutch.
The thing is a LOT of these councils and departments really aren't interested UNTIL you ask for permission - then things change - being loyal public servants they will scoure their legislation & policy and anything else they can find to tell you why you CANNOT do what you want.
In most cases (except mining) its best to ignore the departments and shire and just be discrete in what your doing!
When you find something just keep your trap shut!
Only a few weeks back the maritime museum raided a ouse in Geraldton and recovered coins off the Zyptdorp wreck - that someone had displayed / mounted in their back shed for 30 or more years! Obviously he peed off someone who dobbed him in.
There's an old saying - what the eye doesn't see the heart doesn't desire.
I know few people in this word can keep their trap shut when they find something of worth.
It's human nature after all.
Cheers