You can get hardwood dowels up to at least 1-1/2" OD in most species but I don't know about getting pine dowels. If I were doing it and it was in a conspicuous spot, I would buy a 1" tapered plug cutter for $30 from Woodcraft or Woodworker's Supply, cut the plug from similar pine and epoxy it in, sand and refinish. If it was in an inconspicuous spot, I would buy a 1-1/8" oak dowel, sand a taper on a short length and go from there. The oak dowel would cost about $5 at the same sources.