Why can't I transfer my AU Domain to Shopify?

I need to set up the FROM EMAIL as the email address on the Shopify store is Gmail at the moment and going to spam a lot.

I tried to transfer my domain to Shopify, but it says they do not accept Australian domains .AU

WHY !!! Shopify is more than happy to sell to Australia store owners.

So now I have to pay more for a mail server for the domain, is that correct?

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.