Hi Niv,
Galaxies are very faint so you will need a very sensitive webcam to achieve that, esp in light polluted Sydney.
Your best bet is to use the webcam you have on casual basis on bright objects such as the moon and planets. Can you control the sensitivity of the camera such as gain, exposure etc?
If you can spare $50-80, you can get a QucikCam Pro or a Philips webcam,
http://nightskyinfocus.com/tag/logitech-4000/ they have quite sensitive chips on them, which you can do webcam planetary imaging. There are quite a lot of resources out there showing you how they are done.
For DSOs like galaxies, you either have to get your webcam modified into long exposure capabilities, like this
http://www.home.zonnet.nl/m.m.j.meij...Y/spc900nc.htm , or use other cameras such as a DSLR or dedicated astro camera.
Sorry but there are no shortcuts to astro imaging
Bo