Paramedics found Eliza-Mae dead when they arrived at the house in Pontyberem that Sharon John and Patric Mullane share, the Daily Mirror reported. Police seized Mullane's dog, which neighbors said he acquired several months ago.
The baby's injuries were described as "terrible."
Patricia Punter, who lives next door, said she heard John screaming.
"I don't know what to do," Punter quoted John as saying. "The dog ate my baby's head."
Alaskan malamutes are often used as sled dogs in the Arctic. They are a large breed.
Neighbors said Mullane's dog, named Nisha, usually appeared to be gentle.
"It seemed like a lovely, friendly thing," said Ann Williams, who told the Mirror she let her 3-year-old granddaughter pet Nisha. "I'd never have dreamt it could be capable of anything like this."
Eliza-Mae was the second young child killed by a dog in less than two weeks in England and Wales. An 11-month-old girl was killed in Blackburn by a pit bull nine days ago.