You can add both domains to your Shopify admin. Once you have, you can set the .com.au as your primary domain. From here, you’ll have two options:
Redirect all traffic to this domain - Meaning that if the customer puts in “.com”, they’ll be directed to your store, but the URL will update to your “.com.au” URL
Don’t redirect all traffic - Meaning that if your customer puts in “.com”, they’ll only see “.com” as the URL will not be updated to your primary domain. However; they will still be led to the same store.
Either route will work but if you’re trying to rebrand with the .com.au domain then using the redirect all traffic to this domain will probably be your best route.