Hi,
I just read your post. I think you are still looking for an answer. I have stayed in Melbourne for a year and now I am back to India.
For your initial few days its always better to stay in a serviced apartment or a hotel. Finding a place to rent in Melbourne and suburbs is a big task as the demand is high and supply is less. You can search the same on
www.realestate.com.au.
You have to look for the postings regularly and check when is the place open for inpspection. Mind it that it would only be open for inpsection for an hour or two at the given date and time. If its a good place then trust me, you would always get atleast 10-15 people coming to have a look at the property. If you like the property by having a loook at the website and your investigation then download the application form from the real estate agents website and fill it ( atleast the basic details) and deposit its to the agent at the site itself , else you have to fax it to them or send a scanned copy by email. You have to bid for the rent you want to pay for the place.
Agent will send all the forms to the property owner and they wd make a decision to whom them want to choose.
Its better if you can get a reference letter of the propety agent in dubai (if its a big one) and attach a copy with your rental application.
It is going to help you out. Also carry your bank statemnets, proof of identity, driving licence etc. If possible get a personal reference , it also helps a lot in your selection as a tenent.
If you have any further questions free to ask. I would try to answer your queries.
Regards
VG