This is a wool felt reproduction "Australian Slouch Hat" (official designation "Hat, Khaki, Fur Felt). 

It is believed that this style of hat was first used by the "Victorian Mounted Rifles" based on the head-wear worn by police in Burma.

The Slouch hat was originally an ordinary bush felt hat turned up on the right side to ensure it would not be caught during the drill movement of "Shoulder Arms".

This reproduction comes complete with a seven pleat "Puggaree" and "Rising Sun Badge"

The term ‘puggaree’ originates from the Hindu word, ‘Pagri,’ meaning a turban or thin scarf of muslin. Intended for insulation, the puggaree was a traditional Indian head-wrap, adapted by the British for headdress worn in hot, sunny regions. The seven pleats represent the states and territories of Australia.

The "Rising Sun Badge" has been worn by Australian soldiers since the "First Pattern" was used in 1902.  This reproduction comes complete with a 5th pattern badge used between 1966 and 1972.  This badge has been struck from an original 5th pattern badge with the approval of the Australian "Department of Defence".