That looks like a 2 axel balanced on a single axel, personally I wouldn't be comfortable with towing a 2 axle on a WRX. especially one that weighs a thousand pounds without your toys. With a big trailor like that balancing on one axle you are putting alot fo downward stress on your tow package. Not that its a death sentence but its probablly more than your tow kit was designed tt handle. The only recommendation I can make is upgrade those brakes and make sure your rear suspension is up to the task, sagging 12 year old springs and old struts wont like being loaded down like that. Your essentially driving around with double the weight as OEM. I would just be careful and make sure your brakes are up to the task. As for the trans handling the extra weight its not the gears that take most of the stress. Once your in gear the WRX can handle that load no problem but the clutch definitely wasn't built for that.
In most cases its not the trans that causes problems but the nut behind the wheel that makes things go south in a hurry.
Slow is Smooth > Smooth is Fast