When I heard about a 'loot pet' I assumed it would collect loot or could be used to carry loot in an inventory (like the pack horse in Dungeon Siege) or maybe take it back to town and sell the trash (as in Fate). This pet doesn't appear to do any of that nor does it seem like a minion that you can scale or buff with skills or GoF nodes.

In short, what is its purpose?

Yeah I too am confused as too the true purpose of the pet other than a cosmetic to show off. It doesn't hunt for gold(which is low-tier QoL) nor does it pick up any sort of equiment. I would love if would take a similar system to Torchlight so it can sell the junk items in our bags and return after a minute or so.