Router table with a roundover bit... do each side in turn. To maintain some semblance of control, leave the ends square. I was going to say go to Home Depot, they got plenty of dowels, but then I saw you were in South Africa.
Someone may need to correct me on this, but get a square stick that is twice as big on the side as the diameter of the dowel you want to make. For example, if you want a 1/2" diameter dowel, use a stick that is 1" square and a router bit that is 1/2". I think I would start there and refine the technique.