Also, from just walking around Melbourne and Hobart, it seems that Australian cities are more ownership oriented than major American cities. I've seen maybe 2 "for rent" signs. Am I just not seeing the rentals?
Real estate agents list properties for rent, typically in their windows, on their website, in the newspaper and/or on one or both of the big property websites (RealEstate.com.au and domain.com.au). That's one thing I like: when looking for a rental you only really need to check those two sites.
It's unusual to put a "for rent" (or "for lease") sign up. "For sale" sure.
You can rent something directly from the owner but it's reasonably unusual. Even if the owner finds a tenant they'll typically use a real estate agent to manage the property (do inspections, organize maintenance, take the rent and so on).
So anyway, the lack of rental signs doesn't mean anything. In my experience you only see them in front of larger buildings on the lower end of the economic scale.
The reasons are varied, but increased planning laws and high immigration means that the supply of city properties is not keeping up with demand.
And yes, home ownership is very big in Australia.
It's a lot more common in Australia for people to use property managers, and a lot less common to have large commercial rental properties. I believe gumtree.com.au and housemates.com.au are both popular now.