So it turns out the quest is actually bugged. Just at a different stage. I was finally able to obtain all the required items to turn in the quest. But after turning in this quest your pet gains 10 closeness which works but is supposed to follow you closer and not fall behind anymore, yet its still moving at the same speed as it was before. Also once the quest is complete you're able to pick the quest up again and instantly complete it claiming its given your pet more closeness but nothing happens.
Already reported here: https://royals.ms/forum/threads/quest-bugs.87361/page-2#post-463427 Thanks though!
