Do you think it's possible

[Malzian]

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

Every little bit of exp counts and, as such, I would advocate still doing Ixali through to 60 every day as well. It may not be the biggest chunk of exp, but you still get the reward for turn in plus the easier HQ exp from those quests. You get 9 Beast tribe allowances per day, you can spend 3 on the Moogles, that leaves you with 6 you can use for the Ixali.

Yes, always do GC turn ins and once you're high enough, grinding collectibles is great for experience and gear.