Are you an interior firefighter in Australia? If so, then at the very least, I suggest you carry a pair of linesman pliers or cable cutters. Your life could depend on them someday, and they come in handy on a regular basis.
Many firefighters that use flash hoods don't carry them in their turnout gear. Most of the firefighters in my fully-career department, for example, place them on their boots/pants hitch and don the hood before entering the rig. Others place the hood next to their riding position and don it during the rsponse.
Putting the hood in a pocket just wastes time getting to it for career firefighters.