The parents of six-day-old Eliza-Mae, who is thought to have been killed by the family dog, said they will "cherish the little time we were able to share with her".
Eliza-Mae Mullane was airlifted to the University of Wales Hospital in Cardiff yesterday after what is thought to have been an attack by the family's Alaskan malamute dog.
"Even though she was an important part of our family for such a short period of time, Eliza-Mae will always be in our hearts and thoughts and we will cherish the little time we were able to share with her," Sharon John and Patrick Mullane said in a statement.
"She was a dearly loved daughter, sister, granddaughter and niece. She brought joy into our family, and losing her like this has cast the most horrible shadow over all of us.
"There are no words we can use to describe what we feel at the moment, and we don't think there ever will be."
The Alaskan Malamute, the breed of dog seized from a family home following the death of a six-day-old girl, are large and powerful, but have kind and affectionate natures, according to an expert from The Kennel Club.
"They often live in family situations and are extremely loyal," Bill Lambert, the club's health and breeder services manager said.
He confirmed that the breed is not listed under the Dangerous Dogs Act, adding:
The list demonises certain breeds of dog, and we have to look far deeper than that.
The Dangerous Dogs Act is all about the appearance of the dog, and actually ownership and training of the dog is more important. Any large, powerful dog does have the capacity to cause harm.
The Alaskan Malamute is a Husky-type dog "bred originally for pulling sledges, and they weigh, fully grown, something like 75 to 85 pounds."
Chief Inspector Ieuan Matthews, of Dyfed Powys Police, said specially-trained family liaison officers are supporting the family of a six-day-old baby girl, found dead at a property in Pontyberem, Carmarthenshire.
"As you can imagine, the family are hugely distressed," he said.
Police have confirmed that the infant who died at a property in the Carmarthenshire village of Pontyberem this morning was a baby girl aged six days old.
We are investigating the sudden death of a baby at a property in New Road, Pontyberem.
The baby girl was just six days old.
We were called by the Welsh Ambulance NHS Trust just before 8.30am this morning, and the baby was taken by heli-med to the Heath Hospital. Sadly she was later pronounced dead at University of Wales Hospital in Cardiff.
Our sympathies are with the family at this tragic time and we have specialist officers who are supporting them. All I would ask is that you give them time and space to grieve.
As far as our enquiries are concerned, the investigation is still at an early stage.