I am not a Melbourne local but you really should advise which part of Melbourne you're in. It's just because Melbourne is so geographically spread out and you'd usually only want to find local groups near you.
There will be groups all over the place and usually around in the universities.
Also have a look on Facebook for badminton groups. There is one in Clayton (south east of the city?) under the name badminton connect which it's a social group which you can join in Facebook.