Here is the Royal Arcade that connects (I think) Little Collins Street and Bourke Street.
I also found the more-familiar mall format. There are two big department stores on Collins Street- Myer and David Jones- that are comparable to Nordstrom. To my surprise, these stores opened up to a large mall behind them. Here are a few pictures:
All along Collins Street there are high-end free standing shops like Tiffany and Co., Louis Vuitton, and I even found an Ugg store!
Side note: when I tried to type "grey day" my phone autocorrected to g'day. Which is a phrase Australians actually use, believe it or not. They also greet you by saying "how are you going?" Or just "how you going?" Peter and I haven't really figured out what the correct response to that is yet. Usually we just smile and say "hi."