On the assumption that Jim is right, and your circle is already cut and you simply want to add a profile to the edge, then your problem is one of work holding. Personally I wouldn't fancy freehanding round a piece that small, but it would be a doddle in a router table with a bearing guided bit.
Router tables don't have to be fancy, you can knock something up in minutes to do basic stuff. All you need is a flat bit of MDF with a hole in the middle and the router base screwed of clamped to it with the bit poking through the hole. Then just turn it over and clamp the "table" in a workmate or similar and make sure your cut is ALWAYS AGAINST THE DIRECTION OF ROTATION, otherwise the workpiece along with your fingers will be sucked into the cutter. There is at least one member on well qualified to explain the consequences of getting the last bit wrong.