Is it permissible to kill a small dog that has been bitten by another dog, for fear that the biting dog might be infected with rabies?

Keeping and owning dogs is forbidden, except for a religiously permissible need, such as hunting, farming, or guarding livestock. Otherwise, a qiraṭ (a measure of reward) will be deducted from its owner's reward every day. It is not permissible to kill the dog merely for what you mentioned; rather, it can be kept after being examined by a veterinarian. The Prophet, peace and blessings be upon him, forbade killing dogs, except for the jet-black dog with two spots, for it is a devil.