The best way to propagate red twig dogwoods is by transplanting the suckers, or shoots, that come up around the parent plant. These young shoots already have roots so you can immediately replant and water.
Alternatively, you can propagate by hardwood cuttings (live stakes) in the fall directly in the ground. Any portion of branch that is in contact with the ground will develop new roots. Hardwood cuttings (taken from the previous year's growth) should be 8-12 inches long and have at least 4 nodes. When obtaining cuttings, cut just above a node on the parent plant. Before planting the live stake in the ground make a slanted cut just below a node, dip it in rooting hormone and plant it far enough in the ground so that at least two of the nodes are below ground.
Lastly, you can take softwood cuttings in summer (june) and root them in a small pot as you proposed. If the stem breaks with a characteristic snapping sound, it is in the softwood stage and ready to be harvested as a cutting. By fall they should have developed sufficient roots to survive the winter.
For more information on hardwood and softwood cuttings, please visit the following link: