US Airspace:

Australian airspace (for the most part where we fly (not including the Bogong
Cup)):

In the US we fly in Class E (controlled) airspace. In Australia for the most part we fly in
Class G (uncontrolled) airspace.

US airspace definitions found
here and
here.

Class G airspace includes all airspace not otherwise classified
below flight level 600. There are no entry or clearance requirements for Class G
airspace, even for IFR operations. Class G airspace is typically the airspace
very near the ground (1200 feet or less), beneath Class E airspace.

Radio communication is not required in Class G airspace, even for IFR
operations. Class G is completely uncontrolled.

It should be noted that there are certain exceptions where Class G is extended
above 1,200 feet (370 m) AGL. This is usually either over very mountainous
terrain (i.e. some areas in the Rocky Mountains), or very sparse areas (i.e.,
some parts of Montana.)

Australian airspace definitions are found
here
and here.

However, much of the Australian airspace below 18,000 feet above
mean sea level (amsl) is classified as Class G and not controlled. This airspace
is where most recreational aircraft generally operate.

Australia, it's a lot like Montana!

Here is the Australian airspace in the area used for the Bogong Cup:

We can fly in Class E airspace in Australia (and in the US).