I am curious to learn whether you will have only a single puppet that fights for you (kinda like a DRG's Wyvern) or if you will aquire multiple types of puppets (akin to a SMN having multiple Avatars available or BST jug pets.) from which you can choose.
I think the later option would be more interesting. I would like to see different job types of puppets that are questable. For example, after completing such and such quest you have the power to call a WAR type puppet or SAM type puppet etc. Would give flexibility to fill many different XP job slots.
My main concern about that would be that they would need to have the Puppet's be reasonably balanced against the main job counterparts. Otherwise you pigeonhole the job into a specific role for example "Puppet DoT > THF, therefore the invite THF instead" or "Puppets are only good for nuking" etc. If they are subpar consider how RDMs were seen before their enfeebling skill was raised and convert/refresh added. They were pure generalists subpar to any other job in every role and therefore frowned upon.