Joey, are you sure your spear-line is threaded correctly? RA are normally very good about such things. Also, 3cm is way too short for an RA bungee. BTW Which model did you get - the Sparid perhaps? - most (/all others?) come with a heavy-duty bungee with "big game" swivel & clip. Mono-filament usually has quite a lot of stretch in it, even without a bungee - but a bungee makes stretching the line easier & helps protect the spear-line when you catch a fish.
Hang-on though - you say you have a snap clip...the snap clip on RA is usually part of the bungee. Sounds like you just have some cord holding a clip to the muzzle - doesn't sound like RA - is this a used rail-gun, rather than new? Sounds like you could either replace the spear-line or maybe lengthen the cord holding the muzzle clip. A bungee is a good idea though.
RA 2mm Mako spear-line is very strong (400lb+?). Overkill for us in the UK but it last very well and withstands even quite major nicks and abrasions. For the UK, I usually aim to get 1.65-1.8mm monofilament -- the diameter (for abrasion resistance) is more important here because our fish are relatively modest; I certainly would not go down to 0.8mm - I've seen too many deep cuts and abrasions in my spear-lines (usually near the spear end). You get some big fish in Oz though, so perhaps the 2mm Mako line & big-game bungee will make sense for you.
In your part of the world Adrenaline in Australia or Ron's Corner in NZ can probably provide parts (Ron is an active forum member here, usually very helpful).
RE. bungees, I like the RA Bungee (other rail-gun companies - such as Rabitech/Make, Hammerhead, Pelaj - probably offer similar heavy duty products; Riffe too) but its quite heavy duty. Great if you must deal with big fish. However, with my Omer XXV lightweight rig that I use most currently, I prefer the very trim, cheap & cheerful Beuchat bungee - it uses smaller diameter rubber and the clip on this is much, much lighter-weight that the RA (a tad too light for my tastes) but in keeping with the lightweight gun & smaller fish concerned. I think the Omer & cool looking Imersion shock absorbers probably fall somewhere between the two extremes. apnea.co.uk and scubaland.fr both offer a range of bungees - or "shock absorbers" as they sometimes call them - from different suppliers. The Omer bungees look like good mid-size general purpose bungees. Shop around, you occasionally see bungees at ridiculously high prices, these are quite simple, consumable pieces of kit that should be relatively inexpensive; and you can make them yourself in various ways.