I did this when I arrived in Perth a month ago.
The first thing I did when I arrived was to go to the telstra shop and get one of the mobile wifi devices. Think it was $149 and that included a data allowance. Was really easy to do - I paid in cash and needed my passport as ID then you just top up as you run out of data. The signal is good and I've always had 4g. That said the download speeds vary significantly so at times even though it might say 4g, the speeds will be no better than 3G. The data packs are expensive as well. The device is battery powered as well which is handy when you need to be out using google maps etc.
When I came to get a SIM card a couple of weeks later I ended up going to Vodafone and I've found them far better than telstra. The signal coverage isn't as good so if you're living further out its a consideration. But I've never had less than 3G and the speeds are consistent. I paid $30 a month on a month by month contract for which the equivalent was $49 on telstra. Again, all I needed was passport and bank account details. They said I could email proof of address when that came through. So I'd definitely recommend Vodafone unless you're out in the sticks. Worth going into the store as they have deals not on the internet.
Have you bought your ipad yet? When I was in there, for the money I am spending on telstra data, I could have signed up with Vodafone and they give you a free ipad or ipad mini. When the ipad minis are updated I think I'll be ditching my telstra device and signing up for one