I think thats a great idea. The dog would be a minor DD, and support through skills.

For instance you can have the dog:
"tackle" and stun the target.
"Growl" and have a short duration paralyze
"howl" and give an attack bonus
"bark" to act as a provoke.
and "retrieve" to be used as a pulling tool.

Ninja can still use ninjitsu magic and dual wield.

I think that it's a perfect addition to make the job new for a new FF game.