It's been a while since I played Torchlight, but I seem to recall that my pet would sort of randomly cast the 'Heal All' skill, and the 'Summon Skeletal Archers' skill that I'd given him. It seemed like every twenty seconds or whatever, he'd cast one of them again, so this leads me to believe the pet is still affected by the natural cooldown period of whichever spells you decide to give him.
Based on this, does equipping your pet with things that give a 'faster cast speed' bonus make him able to cast his spells more quickly? I never noticed any improvement myself, but since I assumed it wouldn't work, I never gave him more than probably a 4% bonus in this area. I'm not even sure if this bonus affects spells with a timed cooldown used by the player.