It's not just fashion and cosmetics, things like lawn mowers were also getting imported.
Part of the problem was AUD appreciation which put the MSRP of most things a good 50% above the rest of the world. Coupled with high costs in Australia (due to tight labour legislation which helps sustain an egalitarian culture), no Australian retailer could compete. The AUD has weakened substantially since then so I wonder if the picture has changed enough to make GST matter.
Charging GST might help a little bit, but the issue is FX, high local costs, and relatively cheap international shipping. For example, ASOS offers free international shipping so long as you are ready to wait 4 weeks. This is fine with most customers who prefer buying the same jeans for $60 and wait to paying twice as much and having them instantly. They employ only a handful of people in Australia to manage inbound shipments and customs, but it is (was, 3 years ago when I last looked) a significant chunk of their global profits.
That being said, protectionism didn't work out for the Australian car industry.
[1] http://globalmarketsresearch.commbank.com.au/ReportWeb/d13de...