Not too sure how much control you have using shopify but the normal route is to create country folders so
yourdomain.com/au/category/product
yourdomain.com/nz/category/product
then yes you use hreflang to show which one is for which country. This allows you to run 1 site but includes country-specific content on each page. For example if I was running a site targeting USA and UK my UK site I would be spelling things like colour on the UK version but color on the USA version. Prices on the UK version would be GBP but the USA site USD. etc
There is a lot to think about when going after new countries and depending on your niche this can be quite complex. Please give it some detailed thought before rushing ahead. You have to think as if it was a bricks and mortar business, operating in other countries comes with its own rules.