That would be Dr Tunbridge at 35 Collins St. He has been around so long he probably signed off medicals for the Wright brothers. Dr Tunbridge does my medicals and I think he's great.
My son goes to the DAME at the High St Medical Centre in Prahran and said he is very good too. This guy also specialises in skin cancer work, so you can get a check for that while you're getting your Class 1 done.