Yes, under California law, you would have a potential claim for both.

If the dog bite injury occurred during the course of your normal work duties, you will most likely be able to file a claim for California workers' compensation with your employer. In addition to your workers' compensation claim, if the owner of the dog is not your employer, you may be able to bring a legal claim against that person as well; thus, you would have two claims.  You would definitely need legal counsel to explain more details as to having these two claims.