I've recently gotten back into Oblivion after playing Fallout 3 for a while. One of the mods I use for Oblivion is CM Partners, which adds NPCs and creatures that you can recruit as your companions, so the concept is doable as far as that goes. To issue commands, you crouch (sneak) and activate the creature.

What I'm wondering is if there's a mod out there that adds a creature companion that can look for items for you in the manner that Dogmeat from Fallout 3 does - the whole "Find Ammo (arrows for Oblivion)" "Find Food (Ingredients)" "Find Meds (potions)" "Find Weapons" options that Dogmeat has.

Yes that there is... http://www.gamesas.com/bgsforums/index.php?showtopic=1024988&hl=... which has those kind of options (set up as skills you have to train your pet).
Pacific Morrowind

http://tesnexus.com/downloads/file.php?id=21950.