We just converted our fireplace back into a wood-burning one. When we discovered there was a matching hearth already under the carpet, it was suggested to us to cut it out and use it. Unfortunately, when the person doing the cutting started, he thought he was cutting around a border. He was actually cutting on the outside of carpet bar. Now we have this large gap around the hearth, and we aren't sure how to fix it. What can be put over the gap? 
Although it may be a tad more complicated than plastic or vinyl, I would go with metal. Milled door sills are often produced in 80-100cm lengths (approx. 3'), either with screw holes or simply to be glued in place. You would have to cut it into short lengths with slightly angled ends; in essence you will be constructing a polygon instead of a circle. With a little searching, you will probably find a profile that combines well with the stone on one side, and carpet on the other.
The rationale behind using metal is to create a supplementary barrier for any sparks that may fly with the glass open (e.g. when stirring the fire) and roll on the stone. I would also think some bronze would fit in rather well with your fireplace and poker holder, though that is of course a matter of personal taste.
There are bendable vinyl moldings that you could use to finish off that edge and cover the cut carpet. It may take some searching around to find the right size and shape.
Another cool option would be to use short pieces of complementary marble tile molding in a curve around the hearth (like what I call "horse teeth"), then grout the gaps.
