So far, i think these pets are only offered as rewards upon completing an objective or can be purchased.
I think it would be neat to have some pets that are rare and hard to obtain.

In Final Fantasy VII it was possible to catch Chocobo's with Gysal Greens. I think it could be interesting to have some of these pets spawn in the open world. They could despawn after very short periods of time, perhaps. All you would need to do is get close enough and click on them. They could spawn linked to a linked group of monsters. Claiming the monsters, establishing a claim on the pet. Making it to where, if the battle is won, only the victor can claim the pet. Different types of pets can be native to different regions and could consist of different color variations. To increase the rarity value of a pet, the possible spawn area would have to be very large and the frequency of spawns should be limited as well. (something like every 72 hrs) The spawns could be related to weather events as well.

Kinda like an NM from FFXI.