Y'all can stop with the constant check the yellow sticker, 1/2 tons can't tow anything diatribes.
It really is a little weird.
OP, yes you can tow a smaller to moderate trailer with a 1/2 ton suburban safely.
No it won't win races, it won't like big hills or altitude as much as a truck with twice the power, but properly set up with trailer brakes and likely a wdh and tow away.
The question we should be asking or you should be asking yourself is how good of mechanical condition is your 15 year old vehicle? That will be the biggest variable in whether it's a good decision for that vehicle.
Edit: and an aftermarket transmission cooler if you're going to be towing in hot weather.
There's a few things you'll likely need to do to make it a better tow rig but it will work.