That's an Australian slouch hat, it's a piece of the Australian army uniform. Wide brimmed hats were adopted by Australian armed forces for their protection in the Australian climate but on a parade ground the hat's brim interferes with the shouldering of a rifle. For this reason the ubiquitous slouch hat was adopted. With the formation of the First Australian Imperial Force, the brim of the hat was secured by the Rising Sun badge of the Australian Army. Before the Gallipoli invasion, Australian soldiers were issued with the peaked caps worn by the British. These offered no protection from the sun and Australian soldiers quickly switched back to their slouch hats, as seen in Battlefield 1. While the slouch hat was worn with the side secured as seen in the picture, typically, Australian soldiers wore with the side down for protection from the sun and because the Rising Sun badges often got lost or broken in the front lines. The picture suggests that the hat is rigid and possibly made of leather which it would have to be to hold the shape but in reality they were made of felt and cloth.

It is likely that the decision was made to depict this character wearing the hat like he is because it clearly makes him out to be an Australian...as if the accent wasn't enough.