Given your parameters, a genioplasty would be fine. But the advancement has to consider the narrowness of your face/jaw; so that the overall look does not get compromised when viewing from the front as opposed to profile. Tapered narrow jaws often need augmentation of the area behind the chin as...
You are referring to a slightly convex facial profile which looks aesthetically better on a female than a male. This can be improved by chin augmentation using either an implant or a sliding genioplasty. There are advantages and disadvantages with either technique.
It does appear that you have a recessed chin and some excess fatty tissue under your chin/ jaw. A chin implant will help improve your profile by projecting your chin and it will also stretch the tissue under your chin as well creating a small amount of improvement in your neck. The best result...