Service Central has a bunch of pre-qualified and rated plumbers in Balwyn. Including the Plumbing Professor who has had 110 customers give them a 5 star rating, and Gipps Plumbing who has a 5 star rating after 10 customers.
I've called upon a plumber a few times since moving to Balwyn in 2010. Most recently I used Taylor & Sons. They knew what they were talking about, were quick and very tidy. I strongly recommend them.