I have many contacts at Bairnsdale airport if you wish to contact someone for further information. Some of them have been there for many years. There's an Aeroclub there (East Gippsland Aero Club) and a very friendly bunch of people.
There are no issues getting into Bairnsdale through East Sale Military Control Zone. You will need to be qualified to transit CTA, which is no problem for you.
You can either track via the VFR lanes in contact with East Sale Approach etc or you can usually track direct on a clearance. Personally I've probably flown through there 100 times VFR and never used the VFR lane. If you are using the VFR lane from Bairnsdale back to Melbourne, make sure you don't follow the highway at Stratford, otherwise you'll head straight towards East Sale and they will get unhappy!
They do tend to like the terminology there, "VFR transit, VFR arrival and VFR departure." In your case, it would be a VFR transit.