A quick answer for now as I don't have much time, but I think in Sydney your best bet would be to try and join up a high level Suburban Rugby club. These clubs are more likely to accept players mid season (season usually starts in late March).
You won't get into the Premier Division, which are the top suburban clubs, basically the level below the Super 14 provincial sides. They are semi-professional, at least for their top 2 grades, and would already have started training so getting in is difficult. Although you might be able to get a spot in a 4th or 5th grade side.
The top level "subbies" teams are quite serious about their rugby, but this level really allows a better social scene as well because it is a little more relaxed, you will get a good feel for Aussie rugby culture!
Go to http://www.rugby.net.au/ , which is the NSW Suburban Rugby site to find out about all of the clubs etc. If you know where in Sydney you are going to stay let me know and I can point you in the right direction of a club in your area.