Shoalhaven River

https://en.wikipedia.org/wiki/Styx_River_(Tasmania)

More pictures

More candidates:

https://en.wikipedia.org/wiki/Styx_River_(disambiguation)

There are few candidates. I'd go for the one in Tasmania: it is the longest, the pictures are great and Tasmania is part of Australia.

Plus the mythological version of River Styx! No vote needed

Agree this is the perfect name!