Australia is not part of The Ring of Fire.

The ring of fire is where the world's most active volcanoes lie, it is also where the most earthquakes happen due to tectonic plates rubbing together. People most at risk from volcanic eruptions and earthquakes live in countries that lie along the Ring of Fire which include Chile, Japan, the US west coast, Indonesia, Canada, and New Zealand.

Australian volcanoes on the mainland have never erupted since European settlement, but some volcanoes in Victoria, South Australia, and North Queensland were witnessed by Aboriginal people several thousand years ago.

Australia does experience some earthquakes, but not many.

More Info: en.wikipedia.org