"The Billup's said Buddy disappeared. I found the grave son."
Buddy was the name of the Morgans' next door neighbors' (the Billups) dog. The dog barked for an entire night while Doris Morgan, Dexter's foster mother was sick and it kept her awake. The next morning, the Billups reported the dog missing. Dexter had killed the animal and buried it, along with several other animals that he had killed previously.
Harry Morgan found the grave soon enough and this led to him finding out that Dexter was a budding serial killer, which enabled him to catch Dexter before he went too far. Dexter, as a child, said that "The dog was a noisy little creep dad. He was barking all night and mom couldn't sleep and she's very sick." This kill was the first true sign of Dexter's dark urges. However, he the latter was soon able to channel it using The Code of Harry, and afterwards, Dexter only targeted wicked people, because killing dogs wouldn't have been so productive.