Am I entitled to a hire car if I'm in a not at fault accident?

So the situation explained: I came out from the gym one morning to my car parked within a shopping mall. I had noticed that someone had scraped the paint off the car on the driver's side of the bumper. Turns out long story short, the car next to me had reversed into it when attempting to park, evidently shown by the orange paint attached to their rear bumper. The owner of the car wasn't aware obviously as they had walked off to do their shopping and left their car there.

After a couple of hours of waiting the owner of the car came out and I confronted them much to their denial (i have a dashcam so good luck to anyone who denies they're not at fault). Eventually they agreed to pay the damages privately with no insurance involved which I also agreed to.

The pannel beaters have said the job to fix everything will take three days in which 2 of those days i need a car to get to and from my work.

Should I be able to make a fair case for that person to pay themselves for my hire car? Anything I can say to force their hand if they get argumentitive? For the record I live in Australia, New South Wales.