Good luck! $800/fortnight is very low for anything decent in the area you are wanting to live. You really need 50% more rent than that for a desirable apt. Sydney has close to 0 vacancy rate, and this means you must rent within an hour of finding something -- it will be gone by the next day. Plus you will need references, which might be tough to get, for all the nice apartments. I rented a 1BR for 1 month in November 2010, for $4000 per fortnight, as a point of reference; it was OK, but nothing spectacular (good location with harbour view and parking -- hence the price). Sydney has some of the highest apt prices in the world, it makes NYC and Toronto seem cheap. Even short-term rentals are in short supply; you can always get a serviced apt, but these run $100-200 per day, or more than double your budget.

Cheaper housing is readily available, in the Western suburbs, but it is an hour or 2 train ride away ... hence the lower price. For the prime areas, which you seem set on, expect to have no choice and high price. You can try looking on http://www.gumtree.com.au