When the Australian army introduced the DPCU uniform in the late 1980s, they also introduced a new form of headgear. This was a peaked cap, with a distinctive neck curtain that was officially called the kepi:
The cap has a broad peak to keep the sun out of the wearer’s eyes, this has a stiffener to it and rows of stitching to help keep it firm:
The back of the cap has a small piece of elastic to help keep it securely on the head and allow a small amount of adjustment to cater for varied head sizes:
Whilst the curtain can be worn down to protect the neck from the sun, it can also be folded up inside to allow the cap to be worn as more of a baseball cap:
This particular cap dates from 1992 and has a stores label sewn into the inside:
The kepi is very much an operational piece of uniform and the Australian Army’s dress regulations give these rules on its wear:
Kepi
3.80 The Kepi is worn with Field Dress (DPCU) only by members of units which operate armoured vehicles and personnel posted to Regional Force Surveillance Units. The kepi is not to be worn in public or the barracks environment as a substitute for other forms of barracks headdress, unless participating in field training related activities.
A variation of the cap can be seen here being worn by a member of the Australian military whilst on exercise:
Tales from the Supply Depot 
The design of these, particularly the neck flap and peak combination, look very similar to the (government mandated, and I assume produced) hats that are part of regulation school uniform in Australia, and also to some similar hats mandated for wear by “Tradies” working in an Australian official capacity – council road workers and the like. I’d imagine a similar set of official guidelines produced both.