A prisoner in the living quarters will tell you in passing that Bob is looking for you. When you go through the nearby door to see him, a scene with a rabid dog will play. Defeat the dog to have this side quest show up in your log. It will say to “Deal with the dog attacks” but hold on with this for a good time yet as we have to gather up a couple other side quests first that will void if you get too far in this quest.

The next part of Mean Dogs is to go see the Kennel Master. When you enter his enclosed space next to the Recruitment office, a large dog will attack him. Put it down and talk with him. Next head into the 

Recruitment Office and mention the sick docs. You will be sent to find a doctor, found in the shower area where you start. When you are talking with the doctor you will have the option to kill all the dogs to be safe, but advocate finding a cure. The log will change to "find a veterinarian". Go to the Mess and either talk with Jey first, or head straight for the cook who used to be a veterinarian. To make a cure he needs 3 samples:

Sample 1/3: Kill a rabid dog in the prisoners lodging area next to Bob.

Sample 2/3: In the Crater Zone area, to the left of the mine entrance. You'll see two dogs and you have to kill both.

Sample 3/3: In the Mutant (Dust) area off Crater Zone.

With all three samples you can head back to the Mess and the cook will start making the cure. He will not finish it while you talk to him, and no amount of waiting will make him. You have to head back to the Crater Zone and trigger a scene where the dog attacks the guard outside the recruitment office. This event will void another side quest, Another Face, if you haven't taken care of that yet.

Once the last dog is dead, head back and pick up the cure. Bring this to the Kennel Master to complete the side quest.