From my experience, all of the make-up artists I work with have trained for between 1-4 years at make-up college or private specialist schools (I could give you the names of them in London, but as you're in Australia it would be of no use...)
They learn different types of make-up skills, such as special effects, TV/Film, period/costume, catwalk and fashion etc. and from that decide which area to specialize in.
They then start to test with photographers to build up their book - and if they want to do make-up at catwalk shows, go to see the agencies who deal with the show production. They can be taken on for a few smaller shows during fashion week, but many make-up artists I know don't want to do this as they are re-creating someone else's look, which isn't so appealing. They might never get to touch a model - some shows have more than 30 make-up artists milling around with nothing to do. Someone like Pat McGrath, will have her team of assistants she works with all the time, and you have to get past them first!
Working on getting fashion and beauty shots and magazine tearsheets in your book will be more beneficial to you than doing catwalk shows. Do these only for fun as agencies (if you decide you want representation) don't value these in a MUA's book unless you are the main artist.
Around half of the younger/newer MUA's I know also work on a beauty counter part-time. This means you can always keep up with new products and buy them at a discount (this can be quite invaluable as you have to have a
huge kit) Some MUA's cases are so heavy I can't lift them!
For lower budget shoots you can also be required to do hair. (I don't like MUA's doing hair, but some jobs require it) so you also need to have skills here.
It's quite a difficult area to find work, in London anyway. There seems to be so many MUA's all going for the same job - I often wonder how one stands out over another.
I heard Pat McGrath was stopped by someone on the street asking "did you do that fabulous make-up yourself?!" and the rest was history...