I wouldn't have thought Barra are to be found as far south as BNE, a Google search reveals:
Distribution
L.calcarifer has a very extensive range in tropical and semi-tropical areas of the Indo-Pacific. Its distribution extends from the Persian Gulf to southern China and southwards to the northern Australia. Within Australia its range extends from the Mary and Maroochy River systems in south-east Queensland northwards around the entire northern coast to Shark Bay in Western Australia.
Visit
http://www.nativefish.asn.au/barramundi.html to see details, including a distribution map.
As far as schools go, it's been too long since I last worked in Brisbane for me to give you any relevant information, save that there used to be several ATPL schools of note.