You need to observe the Gross Vehicle Weight Rating as well. That's the total combined van/trailer/cargo weight. In addition, the trailer rating and hitch rating need to be enough to carry the empty weight of the trailer plus the lumber. Especially with loads like lumber, it's tempting to load the max cubic footage that will fit, but this will almost certainly dangerously exceed the GVWR and risk having the trailer drive the van. Caution is warranted.
TC
Uh...no. Only the trailer tounge weight (around 10 percent of total trailer weight) counts against the tow vehicle Gross Vehicle Weight, as that is the only component that is supported by the tow vehicle's suspension and tires. Hitch rating needs to meet or exceed the projected tounge weight. The trailer itself must not be loaded over its own Gross Vehicle Weight, and the total weight of the loaded trailer must not exceed the maximum permissible tow weight, (which is where things like brakes and steering come in...). If his bumber sez "5000 lb trailer/500 lb tounge weight", and its a full-size one-ton truck or van, he can easily handle a 1,200 - 1,500 lb trailer with 1 & 1/2 tons of wood on it. It will handle much differently, of course. Plus a reciever hitch is a wise upgrade - never hurts to have some insurance...