In order to start this quest, you need to have in your team someone with the Pet Pal trait - e.g. Ifan ben-Mezd. Near the entrance to Caverns you can find a dog by the name of Buddy . Talk to him and you will learn that the guards have taken his friend - Emmie. You can decide to help the animal - the dog will then tell you about the key he was able to take from one of the "kidnappers". It is near the ship's wreckage.
1. Fort Joy - Buddy
2. Fort Joy - entrance to Fort Joy Prison
3. Hidden Alcove - entrance to Holding Cells
Emmie is in the Houndmaster Room in Fort Joy Prison. You can reach her in two ways:
The entrance to Fort Joy Prison  is located right behind the gate guarded by magister Borris. If you did not do this before, obtain the key in order to open it - one of the possible methods is defeating the guards. After the fight you get the key after you search Borris' body.
This option is possible after you complete The Teleporter. Go to Hidden Alcove and teleport your team onto a beach. Then, go to Holding Cells . Inside, you find the Houndmaster who is abusing Delorus. No matter how you conduct the conversation you have a battle to fight. Avoid placing your team directly in the entrance to the chamber - there are oil barrels that the enemies can use against you. After the fight, pick up the key to Fort Joy Prison. It lies next to the place where the Houndmaster initially stood. If you managed to save Delorus, he will reveal the password, which will allow you to avoid fighting magisters Carin and Goa.
Ending 1: Emmie lives
Upon reaching Fort Joy Prison go directly to the Houndmaster's chamber. It is a peculiar place, in which there are four dogs. You can open the room with Buddy's Key. After you enter the chamber you start a conversation with the team member who has previously spoken to Buddy. If you mention Buddy and that he misses Emmie you will avoid fighting the dogs.
Reward: 2200 experience points
Ending 2: Emmie dies
If you do not mention Buddy the dogs will attack you. In particular, pay attention to the dogs with crossbows. They can deal significant damage, thus try to avoid entering the chamber. Consider using the door as an additional obstacle for the enemies.
After completing this task go to the Houndmaster's bedroom. There are several valuable items, e.g. Hundmaster's Crossbow.
Reward: 120 experience points
You can go back and report to Buddy, but you will get no additional reward. Except sad, sad dog...