7500 won't do it? What are you hauling?
That Genesis might work if you can somehow keep the tongue below 1000 lbs. But, from experience, that's really difficult. Ditching the generator would help. My dry tongue weight on the Shockwave trailer in my signature (coincidentally a toy hauler with 9980 gvw) is listed at 987 but in the real world it's north of 1600. Dry weight was 7020, but loaded for camp it weighed 8900 lbs with no water. Things add up pretty quick.
Just be careful and try not to overload your receiver or rear axle. Towing a trailer that heavy with a 1/2 ton wasn't for me, even though I had plenty of power. The truck I have now is an excellent match for my trailer. Good luck.