Levequests have nothing to do with it! I wouldn't suggest starting over, either, there's very little point. If you have, however, decided that you really don't want to be tanking stuff? Go ahead and start a new class on the same character - you'll have a +50% EXP boost, probably lots of spare/old gear you can use, and cross-class skills to benefit from. You can reach level 20-ish in a handful of hours - do your hunting logs, class quests, and a couple FATEs wherever to get to 12-13. Then spam FATEs in western la noscea while waiting on low level dungeons and you'll be at 20 in no time. If you liked the basic style of Marauder but just don't want to tank, I suggest Lancer.
Check your journal to see if you do have a main story quest on hand (It has a very fancy quest icon instead of a standard one). If you don't, go into your completed quest list and look at the main story list to figure out which the most recent you've completed is, and then take a look through this list to figure out where you are. If you just got your Grand Company, you should be somewhere in the level 21-29 list specifically.
