If you want it to turn ....
Attach the head so it bottoms out on the dowel's end. Drill a small hole in the back of the head so it's 1/2" from the end of the dowel for a nail. Push the nail into the hole until it touches the dowel. Rotate the head so it leaves a circular ring mark on the dowel. Remove the dowel and cut all the way around the mark left by the nail, making a shallow groove. Saw the head off the nail and push it into the slot you made. It will retain the dowel in the head. Trim the nail to be flush with the back of the head and add a dab of glue.
Instead of a nail, you could use a smaller diameter dowel OR a screw with machine threads so you can remove it if needed. The slot would have to be as wide as the screw OR file the very end so it's smooth all the around about 1/4" up leaving the threads on the rest of the screw.
The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)
Last edited by woodnthings; 08-16-2017 at 06:01 PM.