We only have one navigable river in the area; the Murray. It would be considered the "Mississippi" river of Oz, being the biggest & longest.
Entering the mouth from the southern ocean is quite a challenge, but once your in there, the river is relatively easy to navigate for about 1000 miles. I hope to get in there for some fresh water cruising sometime in the next year or two.
Here's a video of one boat giving the Murray mouth a go.