Sorry no first-hand knowledge but you will find Melbourne extremely friendly to GF needs. Melbourne is a foodie paradise, and I am certain the GF goods will be very high quality, like everything else! Here are some links you might find useful.
The Queen Victoria Market has an unrivaled selection of shops in their 'Delicatessens' area (make sure you find it, people usually miss it, it is inside near the meat market). I have no doubt they'll be lots of fresh GF options in there. At QVM they also have one vendor that specializes in GF:
http://www.qvm.com.au/shops-and-stalls/invita/
GF bread:
https://www.theurbanlist.com/melbour...read-melbourne
I've heard really good things about the Ethiopian restaurant on this list:
http://thecoeliacplate.com/melbourne...t-gluten-free/
This bakery has locations further outside the city if you end up on a road trip:
http://glutenfree4u.com.au/