When an electrical fire began to rip through Trace Adkins' home in Brentwood, Tenn., on June 4, Adkins' three daughters -- MacKenzie, 13, Brianna, 9, and Trinity, 6 -- were at home with their babysitter. The girls and their babysitter made it out of the home fine, but when Brianna realized that her puppies were still inside, she quickly rushed from the family's meeting spot back into the burning house.

The puppies actually belong to Brianna. She suffers from severe allergies, and her 10-month-old Australian shepherds, Daisy and Bella, are one of the few breeds of dog that do not aggravate her allergies.

Since the dogs are so special to her, she refused to stand by and let them die. "A neighbor tried to stop her," Adkins tells PEOPLE. "But she wouldn't be stopped." The neighbor then went with Brianna and the pair were able to bring the puppies back to safety. Adkins praised his daughter's bravery, telling her, "I'm proud of you. I'm proud of you for the way you saved those puppies."

The dogs are very near and dear to the Adkins family, since the entire family loves animals, but they couldn't own animals until Daisy and Bella came into their lives. "I've always been a guy who's not big on fake dogs – if they're not taller than the top of your boot, they're not a real dog," Adkins jests. "But we ended up with girl dogs!"

The family has now relocated to their farm house outside of Nashville, and even though it has been a struggle, Adkins is still rejoicing that his family and pups are OK. He jokingly says, "We're good. We're fortunate. We don't have any room to put stuff -- but we don't have stuff anymore!"

Watch a Clip of Trace Adkins' Press Conference at CMA Fest

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