under warranty

In general yes. Apple’s worldwide warranty in Macs is 1 year. It might be a little more complicated because there is specific Australian warranty law, but that would require that the purchase be in Australia.

https://www.apple.com/au/legal/statutory-warranty/

There may be some caveats because Macs distributed in some countries may have parts that aren’t available in other countries. They might need to pass on shipping charges or customs duties for the parts. This is the version of the warranty in force in Australia, but these terms are in every version of Mac warranties.

https://www.apple.com/legal/warranty/products/embedded-mac-warranty-rest-of-apac-english.html

Apple reserves the right to change the method by which Apple may provide warranty service to you, and your Apple Product’s eligibility to receive a particular method of service. Service will be limited to the options available in the country where service is requested. Service options, parts availability and response times may vary according to country. You may be responsible for shipping and handling charges if the Apple Product cannot be serviced in the country it is in. If you seek service in a country that is not the country of purchase, you will comply with all applicable import and export laws and regulations and be responsible for all custom duties, V.A.T. and other associated taxes and charges. For international service, Apple may repair or replace Apple Products and parts with comparable Apple Products and parts that comply with local standards.

Yes. Repair coverage is global

Because Apple designs the computer, the operating system, and many applications, Mac is a truly integrated system. And only AppleCare+ gives you one-stop service and support from Apple experts, so most issues can be resolved in a single call.

Quote:

• 24/7 priority access to Apple experts via chat or phone

• Global repair coverage

• Onsite repair for desktop computers: Request that a technician come to your work site3
• Mail-in repair for portable computers3: Mail in your Mac using a prepaid shipping box provided by Apple
• Carry-in repair3: Take your Mac to an Apple Store or other Apple Authorized Service Provider

https://www.apple.com/support/products/mac/