@Pushka, that is correct. I got handed a free packet of 5 tests on New Year's Day in MEL upon arrival on QF10 (the tests were handed out after collecting my bag as I went through customs). A friend arrived in MEL last night flying Emirates. I'll find out if that friend got tests and I have more friends coming back at the end of next week.
The VIC government has ordered 34 million RAT tests, I think, so I wouldn't be that surprised if the RAT tests were handed out indefinitely (or at least until there's plentiful supply available for purchase in stores) in MEL to international arrivals with RAT tests now an option to take some of the burden off PCR testing sites.
I got a text message and an email today reminding me to take the day 1 test (if I hadn't already, which I had already done) and informing me to take another test between day 5 and 7. Only if a RAT comes back positive is a PCR test required. Provided the day 1 test is negative one only needs to isolate at home until getting that result.
With the tests typically the line to show the test is valid (and hopefully a negative result) should come through pretty quickly, but with the test I got the instructions advised to read the result after 15 minutes and before 30 minutes is up. The line to indicate a positive test can take a while, I presume to show up.