Do i need to level up my job? at the same time as I level my toon?

[Niwashi]

What you're thinking of as your character's level is really the level of your current class. Once you start unlocking multiple classes, each will have its own level. So you're a level 24 Archer, but if you unlock Pugilist, you'll start off as a level 1 Pugilist when you equip the Pugilist weapon (a Weathered Hora you'll get from the quest that unlocks the class). Each time you switch classes, you'll switch to the level that that class is at. There's a tab in the Character window for showing you your current levels in all the different classes.

Jobs are a bit different, as they're an extension to the class they're based on. A Bard, for instance, is still a type of Archer, and once unlocked will be whatever level your Archer class is at and use all your Archer skills. In order to unlock Bard, you'll need to be at least level 30 as Archer and at least level 15 as Pugilist. You can be higher than those minimums, but it's generally not recommended to go very much past 30 before unlocking the class's associated job.

The hunting log isn't something you level really, just a list of certain mobs that will give you a bit of extra bonus XP, each one listed with a suggested level at which you could take them on. (You can actually do them before or after the listed level, they'd just be more difficult or easy accordingly.) The only thing leveling-like about it is that you need to complete one tier of 10 log entries before you can open up the next tier.