At least half a year, if it traveled by two clipper ships. A fast clipper could make the run from England to Australia in under 100 days. The wiki article is short, but to the point. http://en.wikipedia.org/wiki/Clipper_route#Outbound

You can get a better overview by Reading Last of the Windjammers by Basil Lubbock.

Clipper ships used to carry reputations almost like professional sports teams. Making fast runs was a big deal, and the fastest, like Cutty Sark were extremely famous. This meant that travel times for these ships are well documented.

This webpage has a brief description of many other clippers and some of their fastest passages. Not all to Australia, but it gives you a good idea of their speed. Clippers could make 350 miles or more in a day under good conditions. They started to appear in meaningful numbers in the 1840s. By 1900 they were almost all phased out in favor of steam ships.

The "SS Great Britain" averaged 60 days each way and was in use on the Australia run by 1850. I've no idea if it was used for post but I think in terms of journey times we can take 60 days as a fast journey ("SS Great Britain" had a reputation as a fast ship).

It seems that the first Steam Ship to arrive in Australian waters was "The Rose" in 1842 so certainly at the start of Queen Victoria's reign, 1837, post would have been carried by sail which was significantly slower then even early steam ships.

One thing that I think is worth mentioning is that if the Australian recipient was not in a port the time to send the letter once it was within Australia might have been significant. Just as an example many centres in Western Queensland had no rail service before the 1880's .