Nick here from Shopify.
There are a few good subscription apps on the Shopify App Store for you to look into using. You can see the ones I like the most below:
You should be able to use them on an Australian store no problem. Regarding what payment gateway to use in Australia, you can use Shopify Payments if that is something which interests you. If it doesn't, you can see the full list of all the gateways Shopify is partnered with in Australia here.
Let me know if you think these apps can and will work for you.
All the best, Nick