It all depends on what you mean by hunting undead. I think a dog would be a great thematic choice. In the real world we have cadaver dogs that can sniff out dead bodies even if they're underground. There's also a fairly common trope that animals can sense ghosts and the like.
It seems likely to me that a religious warrior who has dedicated his life to destroying undead might be rewarded by his deity with a dog that unfailingly senses undead and alerts the hero whenever they draw near. Even a small dog that isn't terribly effective in combat would be quite useful if it alerts the paladin to the ghouls that are still 120 feet away, or the invisible ghost that is in the next room and about to come through the wall.
It seems likely to me that a religious warrior who has dedicated his life to destroying undead might be rewarded by his deity with a dog that unfailingly senses undead and alerts the hero whenever they draw near. Even a small dog that isn't terribly effective in combat would be quite useful if it alerts the paladin to the ghouls that are still 120 feet away, or the invisible ghost that is in the next room and about to come through the wall.