Any 3000 lb. or greater lift truck, with 72" long or longr forks will work for you. Assuming that the load is evenly distributed in it's full length. i.e. 4' x 8' sheets of dry wall.
For what it's worth, carpet warehouses mostly use 5000-6000 lbs. cap. forklifts with a pole and can handle up to 1000 lbs. rolls that are 12-15 feet long.
It is alway best to check this information through an authorized dealer(s) of the brand of fork lift you have or are considering buying. And request they give you the reply in written form. Not all lift trucks are alike.
You need to advise them if you have or are considering a truck that is battery powered, engine powered, equipped with press on solid tires or pneumatic style tires (air filled or solid molded), single or dual front drive tires, any attachments to be installed, make & model of the attachments, type of mast installed on the forklift 2 stage, 3 stage or 4 stage or even a 5 stage mast, length of forks.
As Ed T said you need to provide the length width & height of the load and the center of gravity (the balance point of the load).
This way you will not over buy or under buy what you need and be OSHA compliant.
Ball Parking and Quesstimates might get you close but a mite is also a small insect that can bite hard especially with all these Philadelphia lawyers out there.
it depends on where on that 8 foot pallet the "load center" (center of gravity of the load) is, but I am going to guess about 12000 lb capacity ought to do well enough