Really good question! I'm not too familiar with how Australian taxes work, and one thing I will advise is to contact a local tax official/ accountant in your area to find out which taxes you need to charge exactly.
With this in mind, some taxes you might be liable for within the US is economic Nexus, but that is only for very high amounts of sales in particular states. You can read more about this for international merchants here.
You can find the Shopify help guide for setting up taxes for Australia here.
But I can't stress speaking to a local tax professional enough! Let me know if you have any other questions about this.
Nick | Community Moderator @Shopify
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