There's an easy way to round over the end of a one inch dowel. I was making a childs coat rack for the day care, and needed a way to neatly blunt the end of the pegs.
Start out by chucking a 1/2" round over bit with a bearing into your router table. Flush the bit with the table. Now grab a piece of scrap for a fence and before you clamp it in, lay it into the spinning bit so the fence rests against the bearing. Now clamp the fence so the center of the bit is 1/2" away from the edge of the fence.

Now get yourself a 1" dowell longer than the sum of all the pegs you intend to make. I used a 3' dowell to make four  4" pegs. I wanted the extra so I could keep my hands away from the bit.
Take your dowel and holding it against the fence, slide it into the bit and start rotating the dowel. Keep it moving or it will heat up and burn your pegs. 

Here you can see I've clamped a stop block to my chop saw at 4". Cut your rounded peg off the dowel and go back to the router and make another peg! If the pegs are going in at an angle, you need to cut that angle at this time, then square up the dowel for the next cut. I don't like the idea of cutting the pegs to lenght first, because you would be holding a short piece of dowel very close to the router bit, not safe!