The house we just bought had damage to several of the stair trim pieces of wood from a dog. Here are some pictures I took of my fix. I started with a dowel glued in a hole I drilled, then added fiberglass bondo. I used a rasp and double cut file to shape the bondo after it hardened. Once I had the basic shape, I switched to an all-purpose bondo that went on much thinner. More filing and finally sanding and painting.
Bondo brings back memories of the 200$ car I bought when I was 16. It was white with big rust polka dots Pontiac Tempest before I painted it blue.