On the MLU
http://www.mapleleafup.net/forums/showthread.php?t=17299 and old REMLR
http://www.aulro.com/afvb/remlr-general/136692-logo-needs-identifying-16-ad.html#post1554926forums there were a couple of threads about an insignia on a trailer the member had purchased. The image showed a rodent like creature carrying something over it's shoulder.

d@rk51d3's edit of the original image Last Saturday night I was at the Defence of Sydney Artillery Museum on North Head for a searchlight display and camp out.
After most people had left a couple of us were spending time trying to find the bottom of a bottle of port and the old solders present reminising about their time in the service. Two of the members, artillery sergeants had been members in 16 Air Defence Regiment, moaning how the rapier missile system resulted in the disbanding of their regiment.
During the conversation I enquired about the possibility of the graphic belonging to 16AD, well to my surprise, the old gent not only knew the graphic but also its history. It all related to the US made FIM-43 Redeye shoulder launched missile system. Apparently the system was so bad that the only thing the system was cabable of hitting was someone's lighted cigarette as they stood still a couple of hundred yards away, with it's infra-red defector too poor to lock onto, track and hit a moving aircraft. Hence the rodent carrying the redeye over it's shoulder and the singed tail representing that only the operators were the likely victims of the weapon.