Do you think it's possible

[ZioSerpe]

You can do the following:
Always: Daily GC Turn ins and Leves
1-50: Ixhal Tribe Quests (some of the higher level ones need you to have a Battle class or gatherer at 45 thought)
50-60: Moogle Tribe Quests and Script turn ins

Actually you only need a battle class at 45, which you have anyway, you need a battle class at lvl 45 to unlock them in the first place, for gatherer the nodes are lvl 5, so even if you're level one you can still do them.