you mean displaced?
The salt will flow with the water down stream to somewhere lower lying and get deposited at different locations.
Some might get flushed out to sea, however there's a lot of land of slow flowing water. The distance inland we're talking can be thousands of kilometres. Meaning that salt would be deposited anyway (remember the high evaporation rates), the removal of which could take a very long time.
The next problem you have to deal with massive amounts of flowing water is soil erosion. Which 1) Removes all the fertile top soil and flushes it away
2) causes algal blooms in bodies of water the soil flows into. Some nutrients in the water is fine, but large algal booms cause water de-oxygenation, which kill all the marine life.
No matter how to approach this problem, there's no simple solution that a) doesn't cause problems for other parts of Australia or b) costs so much money and resources that it's infeasible to do.
The best solution to desalination is gradual land rejuvenation over the period of years.
Some land is too far gone however, or will take a very long time to remove the salinity.
Something else to consider is that inland Northern Australia experiences flashfloods every large tropical storm. So what you're talking about already occurs, and yes, does create blooms of flora inland, but that also causes salinity problems in low lying catchments if it is only seasonally wet and completely evaporates.