The law in Australia is clear in this respect: prices should always be quoted including GST. As the Australian Competition & Consumer Commission explains:
When you present prices to your customers, you must state the total price of the good or service as a single figure, which is the minimum total cost that is able to be calculated. This should include any GST, COR, domain registration, or other additional charges. If you promote a price that is only part of the total price, the total price must also be displayed at least as prominently as the part price.
If a seller is quoting a GST exclusive price, it may be trying to attract overseas buyers (who won’t have to pay GST) or business customers (who do have to pay the GST but can offset those costs against their own GST charges). However, that doesn’t make the approach legal.
A better approach, both legally and in terms of customer satisfaction is to quote the full price and then subtract GST at the checkout if the customer is in a location where GST would not apply.