Leveling an undead as your first pet is extremely rough, especially considering the starter zones are almost exclusively rats and frogs. Some humanoid murlocs in Elwynn/Loch Modan would be awfully nice; maybe Hordies could have some humanoid quillboar pets in and around the Barrens.
Once you have a high level pet, it becomes easy to level any other pet by starting the lowbie out against a much higher enemy, then swapping after one action to the high level pet to finish the fight. E.g. while leveling lil KT, I started him against random moths in Hyjal or Jade Forest, or dragonbone hatchlings, then swapped to a level 25 Emerald Whelpling after he took one hit (which he hopefully survived). KT took a lot of damage this way, but he also leveled up after nearly every fight, which healed him to full. Levels 1-10 was only a matter of ~10 fights doing this.
So, I'd say the quickest way to level undead is to level something else first.