The same way you would add any other domain name.
Go to Online Store > Domains > Add your domain name > Connect Existing Domain Name
Once done add the IP address and CNAME to the .COM.AU Registrar in Australia.
This is an accepted solution.
@CMather hit the nail on the head here. You will first need to purchase a .com.au domain from a domain provider (such as GoDaddy) as Shopify is unable to sell .com.au domains. Once done, you can add it to your store and if you wish, make it your primary domain. The .myshopify.com URL will be your default primary domain until you change it.
Do you have any other questions about your store set up? If so, let me know!