Jonathas doesn't give you the unicorn, it's a quest reward by completing the quest with the npc in the CNJ's Guild in Old Gridania.

I'm pretty sure you have to actually be a CNJ when turning in the quest though, as in, you have to unequip your WHM Soul Crystal in order to complete it, as you have to be CNJ and not WHM to flag the quest and undertake it, but that might be the cause of your problem.