Hi Anna - fellow Aussie here.
As a first step, have a look through this site using the search function. There is a LOT of material about seeking work here in SIN.
In considering your options, you might want to think about a few of the following observations we've made. I'm sure others will put in theirs and also their advice as well.
1. In hospitality, and many other industries, there are already a number of Foreigners working here. Consider that while SIN needs a growing workforce, are you prepared to work for the $ the employers are prepared to offer.
2. Consider the legality of your visa status at all times.
3. Check the local jobs forums here, and the local job databases, and guage if you think you can find employment.
Hope this helps!!! P & C