I noticed that when the Shale Spider cast Embrace of the Shale Spider that it spreads an halo of some sort of pixie dust and then you get a visual effect on yourself that lasts a few seconds when you gain the buff.
Spirit Beast Blessing applies the same visual effect that Druids have when in Moonking form using the Astral Form glyph, and the effect is only displayed on the pet for a few seconds, nothing on the Hunter itself unfortunately.
Out of all the pets that give the Stamina buff, only the Bear and Silithid has a visual effect, though the later is the same as on live, which is the same as the old Warlock Imp's Blood Pact.
The Sporebat seems to have a glow added, I don't remember seeing this on live. Correct me if I'm wrong.
Finally, the Fox and Monkey skills that gives them 30% Dodge makes them transparent, similar to the Rogue's Evasion skill.
All the other pet that gives out buffs don't seem to have anything special as far as visual effect goes. Some just do a normal animation, like the Devilsaur will roar, the Hyena will howl, and for some reasons the Tallstrider will walk in place!
The rest don't have any animations nor visual effects at all. Maybe they will get some later on, or maybe not. Either way I think it's a nice little addition to our pets. 
