You are smart to be concerned about moisture in insulation and to look into upgrading insulation in your attic and on ductwork.
There are really three separate issues.
First, most ductwork leaks. This lets conditioned air leak into the attic and for air from the attic to be drawn into the ductwork adding to the heating and cooling load as well as introducing moisture and dust.
Second, ductwork should be sealed using mastic – a sticky paste rather than “duct tape that pulls loose over time. Once ductwork is properly sealed, then adding more duct insulation makes sense.
Finally, duct insulation comes with a foil vapor barrier to prevent moisture from condensing inside the insulation. To be effective, the insulation must be properly installed and the foil vapor barrier must be free of holes and gaps. Separate from duct sealing and insulation, adding more insulation to your attic is straightforward. But like duct sealing, sealing up holes where pipes and wires come thru the ceiling into the attic or around recessed light fixtures and attic access doors should be done first.
You should talk to your local Touchstone Energy cooperative. They can provide more tips and advice and recommend contractors to help with the work.