First, as far as I am aware there is no "American Curriculum". US School curricula are set at a State level so there is no National curriculum, nor is there a national framework like there is in Australia
Second I am not aware of any school in Victoria following the British curriculum, public or private. I am aware of some outside of Victoria... but if there are any in Melbourne your best bet to find them is by ing the British Consulate General in Melbourne. If anyone is going to be able to give you a concrete list it is likely to be them.
That said, there are quite a number of schools both public and private that offer the International Baccalaureate in parallel with the Victorian curriculum.
What are you concerns with the Victorian Curriculum and / or the Australian Framework to which all State Curricula align?