Inverter Generator Watt Question
You will have to look into more detail into your invertor. If the generator is rated at 2000w, then it can handle 1200; however, that rating might be for the AC output and not DC. 

Check to see if it contains any rating specifically for the DC output. If you cannot find this, the invertor will probably be fused; if you can determine the value of the DC fuse then you can establish what wattage the invertor DC output was intended for.