Hello! I was doing my daily Shinwa quest, and she asked me to get an item from Carl. Unfortunately, I have not yet unlocked the Omen Islands, which means that through no fault of my own I can't actually do that. Is this intended behaviour?

Yup, it's intended! Carl's quests are really the only thing of any interest on the Omen Islands and the uncharted map pieces are pretty easy and cheap to get from user shops.

Alright, cool. Thank you!