I was a little disappointed to hear they didn't have one currently, but then I remembered that there weren't any initially in FFXI (At least, I THINK they added Drg later, though they may have had Bst from the start).
I usually end up using these in games (I find Pup from XI very attractive).
So, then I ended up thinking about how it would fit in. If they add spears later, they could include a Drg-like class.
I also thought about "compound" classes that "turn" you into a certain class. Like, having a spear in the main slot and a wyvern collar in the ammo/ranged slot would give you jump skills and a pet.
I also thought about a Bst-like class that would equip whips. With the graphical abilities of the new game, these could finally be viable. I hope it has a permanent pet, though (or maybe a weak perma-pet and the ability to tame others).
I hope that SE decides to put at least one in eventually, preferabbly with varying levels of pet dependency (like in FFXI, but even larger). As a Bst or Pup, your abilities, damage and survival were WAY lower without a pet. As a Smn (at least how players ended up using it) or Drg, it wasn't as bad. Though, it was worse for the latter.
That way, people who really want to invest in the pet have a class and those who just want a partner do as well.