Dog Fur is an item that can be obtained in Red Dead Redemption. This can be sold in a medium value.
Like the horses, killing a dog or a horse is usually dishonorable, especially if they horses or dogs are tamed, even though you can kill wild dog (which are hard to find) general stores will give you money for it. All the general stores usually give you about $5- $8 for the dog fur. The price varies location of the general store.