I can't provide any detail, but I believe that they were called the Australian Army Provost Corps rather than Corps of Military Police. That might help with internet searches, etc.
Yes, it was the Provost Corps. I looked at them when I studied the 9th Div, but I can't give detail on the company organization.
I was in the Royal Australian Army Provost Corps, 1967 to 1973, Reservist, then they were part of Citizens Military Forces - CMF. These days Called Australian Army Reserve. They are now called The Royal Australian Military Police. Re WW2 formations, I do believe a Provost Company was attached to each Australian Division. Post WW2 a Provost Company was attached to each Army Command, i.e. I was in 2 Div Provost Coy, part of Eastern Command (Sydney)