I was just thinking that in Australia, a "tranny cooler" is a Vodka Cruiser on ice held by what appears to be a woman.
I would expect a camper trailer to peak at around 1500Kg. They generally don't like more than about 750Kg per wheel, and since camper trailers are usually exclusively single axles, any more than 1500Kg makes the choice of tyre rather important - you can't use normal off-road tyres, you have to move to LTs.
Since the cops have been pulling over caravans and weighing them (it's not a myth this time) it's something to be very, very careful about. They've been looking at GVM, GCM and caravan's loaded weight alone (GTM). What's misunderstood by many (and not an issue here for the OP) is that the Gross Trailer Mass - the total mass of the trailer - is checked against the max allowed to be towed. They don't subtract the ball weight, BUT the ball weight is added to the tow vehicle's load (GVM) and checked.
It's correct. Example: 2T trailer, 200Kg ball weight. The tow vehicle has to be able to support that 200Kg ball weight on its suspension (not the caravan's suspension). However, the tow vehicle is pulling 2000Kg, not 1800Kg.
Anyone towing up towards their GCM need to take care. A weighbridge costs about $40. The fines are several hundred $ if you're overweight and in some cases they're stopping you from continuing until the weight issue is resolved or the rig gets towed.