Just so you know, if you have any battle class at a higher level than the one you are currently on, you get a 50% XP bonus to enemy kills and some other sources of XP. I'm unsure which but for sure quests aren't one of them.

Anyway my point is grinding monsters for the first few levels will work just fine and dungeons on future classes will be extremely rewarding as enemy kill XP in dungeons is nuts with this bonus and rested XP bonus. Helps make up for the lack of quests!