I am 35 years old going to Australia, not planning to work.
I've understood there are (at least) two different time spans for visas, < 3 months and > 3 months.
What is required to get a visa for 3-6 months, and how long time does it take?
There is an handy wizard to figure out what visa you will need to apply for depending on you duration of stay.
And on the same site there is a page describing standard processing time for various visas, which you can take a look at.