Ah yes the fresh water lobsters we do have here. These ones you refer to as craydads we call Yabbies I think. We have a very black species here in Tasmania and they are protected from being caught.They are quite different to the crayfish, which are salt water creatures.
Actually the fresh water species proper name is crayfish and the salt water is lobster (southern rock lobster in my pic as it's officially known) But we refer to the salt water one as a crayfish and the fresh water as the lobster LOL...who knows why.
So yes we do have the similar fresh water species but the ones we catch in the fishing industry is the salt water species. Clear as mud I'd say LOL.