1/2 ton trucks can often pull the load. It's payload where 1/2 ton trucks typically fail.
If you get a "unicorn" 2500lb payload 1/2 ton, yes, you likely have enough tow rating and enough payload rating.
Your average 1/2 ton truck is somewhere in the vicinity of 1500-1700lb payload and that get's pretty marginal.
Some 1/2 ton trucks have truly pathetic payloads (under 1000lb) and no question they will be over their ratings.
7000lb empty will likely be up around 9000lb full with a hitch weight of around 1200lb. Add in say 500lb for a family of 4 plus cooler, firewood, etc... in the truck bed and you are very quickly going to be asking the truck to carry (ie: payload) 2000lb or more.
So assuming you want to stay within the manufacture ratings, it's unlikely to be half ton towable unless you camp by yourself and take nothing in the truck or trailer.
3/4 ton trucks on the other hand start around 2200-2500lb payload (check the door jamb to see what your payload is). Odds are you are fine with a 3/4 ton.