G'day Baikonour!
I did my conversion from a UK JAR licence last year and L'aviateur's steps are spot on (although I got my documents notarized which added another delay). I have no idea why CASA requires copies of your licence when the CAA confirms it, but anyway!
As you'll see, it's not really (IMO) an option if you are just coming for a few weeks holiday/work. My flight review alone (2.5hrs) cost about $830. Depending on your experience, you'd perhaps need/want some local instruction before doing a flight review to get up to speed with local procedures (I'm relatively low hours and mostly UK cross country experience, so it was quite different for me).
Actually, unless you can do a CASA medical in the UK and get all the paperwork off so you have a CASA licence before arrival, then get over jetlag, be lucky enough to have the right weather and go straight into a flight review, I don't think it's realistically feasible.
Have fun down here - and give us a shout if you visit Victoria!
GF