Only certain domain registrars are allowed to issue or accept transfers of Australian domains, and what Shopify uses isn’t one of those. Shopfiy doesn’t make the rules on that but I do get that it can be frustrating. A long ago (like over 10yrs ago) ago it used to be only MelbourneIT that could issue them so they had quite the strangehold. Thankfully things have opened up but it’s still quite restrictive.
Some registars will give you all your need to host the email, and get setup with Gmail. Though not all do.
Not sure what you got with your domain purchase so it’s a little hard to give much advice.
I would double check what you got in your domain package first just in case it has all you need.