Permanent residents who have an overseas driving license are allowed to drive with their overseas driving license up to 6 months from the time the visa is granted or the first entry to Australia, whichever comes later. At least, this is the rule in Victoria. After that, they have to have a Victorian driving license to drive on the road. Since my first entry to Australia was in October 2015, I had to get my Victorian license before April of 2016.
Note: There was a some confusion as to which date is considered as the first entry to Australia. This is because, in October, I arrived as a temporary visitor, although I used the same visa. In February 2016, I arrived as a migrant. This distinction was only applicable to the immigration at the airport, but for VicRoads, October was my first entry to Australia, and it had to be 6 months from then.
The first step in obtaining the Victorian driving license is to pass the learner permit test and the hazard perception test. They are the same tests you have to take to get your probationary license (one that allows you to drive with someone who has a full license, if you are beginning from the scratch). These tests have to be taken at a VicRoads (that's the governing body for licensing and registration) centre and are computer based.
But first, you have to have a client account at VicRoads. For that, you need to take documents that can prove that you reside in Victoria. This could be a hassle for someone who just moved in, as he does not have a bank statement or a utility bill sent to his current address, which will most likely be his friend’s or relative’s address. The easiest option is to open a bank account and apply for a debit card. If you get the debit card, the letter the card comes in is enough to certify your address as the debit card is always posted to your residential address. I had opened a bank account with Westpac when I was in Japan (yes you can do that, and it is called Westpac Choice for Migrants), and within few days after moving to Australia, I received my first bank statement. It stated I had zero fund, but meh! I took this to VicRoads in Broadmeadows, which was the closest centre to me, and I opened a client account. I applied for the aforementioned tests on on the same day, and I got time slots in two days. There was a 1hr 2hr 30min gap between the two, originally, but on the test date it was possible to take them successively as there were some free slots.
The learner permit test was easy as they ask questions from the booklet (well, I did not buy it; I simply downloaded the PDF from their site for free) and there are ample mock exams on VicRoads website. Same questions seem to get asked at the test, as I had seen the questions that I got for my test before. Deja vu? The hazard perception test was not easy though; not that the questions were hard, but the video was of very low quality (low resolution and low bit-rate). And VicRoads does not have sample questions to practise with, although the South Australian governing body, 'my license' has some sample practice tests on their website.