This page of Assassin's Creed Valhalla guide has a detailed walkthrough of The Doom Book of Cats side quest.
Rewards for completing the quest:
- 1,200 XP;
- Farmer's House Door Key.
In the place marked in the picture above, you will meet a man who complains about the gods who sent rats to his crops.
Near that spot, you will meet a woman who has a key to the room where cats are kept. When you talk to her and have Charisma at least on the second level, she will give you the key to the building.
Open the building and the cats will run out into the field and start killing rats.
Go back to the man to complete this task. You will receive the key to the farmer's house - inside you will find supplies and silver.