Use a program called Calibre (PC / Mac) to manage your Kindle library. Calibre has pre-build feeds for ABC News, Business Spectator, Daily Telegraph, The Age, The Australian, The Sydney Morning Herald, and The West Australian. You can also create your own. It has a news feed option that can get news feeds from different websites and turn it into a Kindle paper.
In order to use this feature, open Calibre, click "Fetch News" -> English (Australia) -> select the newspaper you want to read.
Calibre is constantly updated so button names and layout might change in the future.