From 1948 to 1960 the Australian Regular Army had 1st Brigade and the Citizen Military Forces had 2nd and 3rd Division, but with the Pentropic reorganisation the 1st Division was stood up and 1st Brigade disestablished.
However is unrealistic/presumptuous to stand up a Division by adding an Armoured Car Regiment, a Tank Regiment and perhaps a medium artillery regiment to a 3 battalion Brigade and call it a division? Is this collection of units a bit big to be called a Brigade Group?
Just for perspective a 4th Battalion was stood up in early 1964, the Army was testing tracked APCs in 1963, a cavalry regiment stood up in 1965 so planning for a larger RA was in the wings in 1960.