You may be able to walk into a roads authority in your State and arrange something. In Vic at least it used to be about 10 days for a new card to be issued, but it is possible that they may be able to issue something on the spot given the urgency.

Also I would suggest getting an International Drivers Licence. Many places will required you to have it to rent even if both jurisdictions are English speaking in any event.

 

I just use a screenshot of my digital licence for anything that requires a copy or upload.
Haven't had any issues doing that so far

 

I initially booked a vehicle but the provider said that the digital licence wasn't sufficient and required the card. Although, since posting, I have actually booked with Indigo Car Hire.

I'll post on my return with an update.