Shouldn't be a problem. I have used my GR2120 to move both a pop-up camper (2000 lbs) and and 18 foot boat (3500 lbs) around the yard. Before I had the GR, I did it with an old Toro 520H. The 4WD on the GR makes towing much easier as I get no slippage on damp grass.
Note: you probably already know this, but don't forget to put wood planks under your trailer tires when you park it in the yard as it will sink.