Your link specifies the maximum payload for what usually is a 4x2 base trim regular cab short bed 1/2 ton pickup. If you end up with a 4x4 crew cab in an upper trim, your payload will be way below the maximum payload. Like I've said earlier, I've seen the data plates stamped on the door frame for these vehicles. GM usually does a bit better at 1450-1700lbs. Ram is the lowest usually at 900-1200 lbs for a Limited trim and Ford is around 1350-1500 for a Platinum trim. You're going to want around 15% on the tongue so that's around 1,200 lbs. You're going to use up most of your payload on the tongue weight of a 8,000lbs trailer.
In fact, a flat bed car trailer is one of the easiest types of trailers to optimize because there's little cross section for the wind to cause sway and you can move the towed vehicle forward and backwards to adjust weight. An enclosed car trailer is similar but you have a much larger cross section that can result in more sway. The hardest trailer would be an camper because you can't easily adjust the balance of the trailer to optimize tongue weight as the other 2 trailers.
Ram is the only truck manufacturer with an online payload calculator
by VIN (again, because you'll find that the actual payload for builds varies greatly):
Find everything you need to know about Ram towing capacity, payload & more here. Discover the best Ram truck or van that fits your towing needs today.
www.ramtrucks.com
Ultimately, with a 1/2 ton someone should definitely have the vehicle (as loaded) + trailer over a certified scale to be near 100% sure they're within all the limits (rear axle weight rating + GCWR).