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Use drywall screws to fit one piece of 14" x 9" plywood perpendicular to another of the same size. This creates a V-block fence to use on the router.
Cut the 9" x 2" scrap piece of plywood so that it fits like a shelf inside the V-block. Drill the shelf into place.
Put a rabbeting bit in the router, and raise it until the bottom of the bit is even with the top of the router table.
Place the V-block fence on the router table, positioned so that the router bit is in the center of its joint.
Clamp the V-block into place on the router table's fence.
Turn the router on. Hold the dowel in one hand, and lower the dowel through the shelf on the V-block and into the rotating bit (Image 1).
Rotate the dowel clockwise with the other hand. Keep turning until a tenon has been cut in the end of the dowel to create a new rung (Image 2).