You do not, I repeat do not NEED a dually to pull a 3670. I pulled a 3670RL for 3 1/2 years with a single rear wheel 3500 and was within the truck manufacturer's maximum weights for pin weight (weight in the bed), rear axle, max towing weight, and GCVW, etc. Would a dually be more stable? Sure, because it is wider. Though the dual rear wheel trucks are always rated to carry more weight in the bed, that does not necessarily mean they are always rated by the manufacturer to also tow more weight. In fact, the tow weight rating on my single rear wheel truck is slightly higher than that on a dually from the same year. That's because the extra weight of the dual rear wheel components use up some of what you could have been pulling. If I was towing every weekend, I'd probably want the dual rear wheels, but since I only tow a few times a year & use the truck as a daily driver, the single rear wheel variety is a better compromise for me.
Could you pull the 3670 with a 3/4 ton truck and be within the manufacturers rated numbers? I doubt it. Sure, the 3/4 T trucks sometimes have the same engine, trans, rear end, etc. and COULD pull the 3670, but if you run the numbers you will probably be over on your GCVW. Many will tell you that the 3/4 ton trucks are the same as the 1 ton trucks except for a spring or two. That may be so, but adding airbags or 1 ton springs will not change the original numbers that the manufacturer put on your truck. If you have a 3/4 T truck already, I'd probably make it work, but if you are planning to buy a truck, I would definitely use a 1 ton.
Look at the weight of your trailer & the pin weight and compare that to the numbers for your particular truck & its components to be sure. I love safety margin, but you have to stop somewhere. I mean, I could get a Ford F450, or a F550, or a Freightliner or a ......