Your dually should have either a 23K# a 26K# CGVWR. That's pretty typical of the newer 1 ton dually's.
To be legal you've got to stay under your axle ratings, your tire ratings, have enough tagged weight paid for on your vehicle, and have CDL's if your combined weight of the vehicle and trailer is over 26K#.
One caveat to that in NC and some other states is that a CDL is required if your trailer is rated over 10K# even if your combined weight of truck and trailer is under 26K#.
You are not illegal if you follow the law.
Now, it is illegal to go over your trucks CGVWR. No, if you adhere to the letter of the law.
Is it smart.
You be the judge.
Personally, I would not pull a trailer rated for 22K# with a 1 ton dually even though you can do it legally. That size trailer needs a F450 or F550 IMHO.