Here Kity, Kitty Quest
This quest will be triggered or can be aquired when you complete Vault 81 quest.
Stages of "Here Kity, Kitty" quest
1. Find Ashes
Erin Combes' cat, Ashes, has escaped Vault 81 and is now loose in the Commonwealth. She's asked me to find him and bring him home safely before something happens to him.
Go outside the vault, Ashes should be on the other side of the lake. Go and tell him to go back home.
2. Talk to Erin
I found Ashes out in the Commonwealth and sent him home. Luckily, no harm had come to him. I should find Erin and let her know.