Sorry, but the warranty for an iPhone can be restricted by Apple to the country of purchase, due to the different built in hardware. You'll might have to send the iPhone back to Australia, to get it serviced.
To find out, if there are exceptions if it comes to display replacements, contact the official Apple Support:
Contact Apple for support and service - Apple Support
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IMPORTANT RESTRICTION FOR iPHONE, iPAD, APPLE TV AND HOMEPOD SERVICE.
Apple may restrict warranty service for iPhone, iPad, Apple TV and HomePod to the country where Apple or its Authorized Distributors originally sold the device.
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copied from: Legal - iOS Warranty Rest Of APAC English - Apple