The Australian Science Fiction Bullsheet is a more or less monthly newsletter that is focused on Australian Science Fiction, fantasy, horror, and related genres. It was started in 1994 by Marc Ortlieb who published it monthly up until 2001 (archives here and here). It was then taken over by Edwina Harvey and Ted Scribner who kept it going until 2010. There are theoretically archives for that but the ones at the Fanac site appear to be broken and the Yahoo archive requires you to join the group.
There was then a short hiatus, but it was relaunched in February 2011 by Wendy Palmer, and is in theory published on the first Sunday of each month. There’s an email version, an rss feed, and they’re also on twitter as @sfbullsheet. It now has a site of its own at http://www.bullsheet.sf.org.au/ where the current newsletter and the archives back to the relaunch in 2011 are available.
It is perhaps not strictly a fanzine, but has been bringing genre related news to Australian fans with an Australian focus, nearly continuously for over 15 years now. So if you want to know what is happening in the various speculative genres in Australia, whether in competitions, movies, books, awards and nominations, conventions, or whatever else comes up that month it might be worth a look.