Police said the shooting happened inside the Brookstone Apartment complex in Clayton County about 9:30 a.m. Sunday.
According to police, Young's 27-year-old girlfriend went to his home with a family member to pick up her belongings.
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"It does appear that she was in the process of separating from the relationship. She was attempting to leave," a detective told WSB-TV's Christian Jennings.
The family member told police that the suspect and the woman got into an argument, and then the suspect shot her several times with a handgun.
The woman was able to run away and get help but later died as a result of her injuries, according to police.
A K-9 tried to search for Young, and police said he stabbed the dog twice.
The police dog was taken to a nearby animal hospital, where veterinarians were able to stabilize it.
The K-9 is out of surgery and recovering.
"It's just a horrific incident. Of course our K-9s are considered family. They protect our officers and stand by our side during incidents like this," a detective said.