Most 7,000 Lb trailers (2 - 3500 Lb axles) weigh about 2,000 Lbs empty, so you can only put 5,000 Lbs on it, at most ... Not including what is on the tongue.
Sounds to me like a 10,000 Lb rated trailer would be better for you, weighs about 3,000 Lbs empty ... I'd not get less than 20' and if...