May be that you're being confused by the map projection[0] -- South America is much much closer than Australia, and you can also take a direct flight there.
LHR - Rio: 5,734 mi, and it's a direct flight. 11-12 hours ish in the air.
LHR - Perth: 9,009 mi, and it wasn't possible as a direct flight when the map was made, meaning you'd be doing pretty well to get it done in under 20 hours, assuming Perth is even your best jumping-off point. You're looking at another three hours to get to SYD or MEL.
Once there, there are no shortage of airstrips in central Brazil.
[0] http://www.gcmap.com/mapui?P=GIG-LHR-PER