Your Hunting Log will be in your menus. You do have it - it was given by your level 5 class quest on your initial class.

Hunting Log, a couple FATEs, and your class quests will get you levelled up in a class in no time, at least to the ~12-13 mark. Push to 15 through a bit more work with FATEs (each region has FATEs in that level range, though West La Noscea is the most commonly used) and you can start levelling in dungeons.