The child, who was from Glasvey Drive, Twinbrook, was injured on Wednesday and had been taken to the Royal Victoria Hospital in Belfast in a critical condition.
Police said a post-mortem examination will be carried out in the coming days.
Earlier on Friday, the girl's 23-year-old father Christopher O'Neill, who is from west Belfast, appeared at Craigavon Magistrates' Court charged with causing grievous bodily harm to his daughter.
Little Cárágh had sustained what police described in court as a "significant traumatic brain injury" and was bleeding onto her brain.
After she was taken to the Royal Victoria Hospital on Wednesday "unconscious and not breathing," a CT scan revealed subarachnoid and subdural bleeding, the detective constable told the court on Friday.
Appearing in the dock of the court in jeans and a grey checked shirt, her father spoke only to confirm his name but throughout the 10 minute hearing, sat with his head bowed, staring at the floor.
He is accused of causing grievous bodily harm to his three-month-old daughter Cárágh on Wednesday 5 February this year and the court heard that during police interviews, he admitted to "shaking" his baby daughter.
Objecting to a bail application, a detective constable revealed that she has suffered subarachnoid and subdural bleeding into her brain in what he repeatedly described as a "tragic case".
The officer described how the baby's father and mother had been going out for 18 months, but had moved in together to an apartment in west Belfast just five days ago.
The officer outlined how on Wednesday morning, baby Cárágh had arrived at the Royal Victoria Hospital "unconscious and not breathing," adding that medical alerted police to the baby's injuries when they were not satisfied with the explanation for her injuries.
"The preliminary findings of a CT scan of her brain found that she had suffered a significant traumatic brain injury," said the officer, telling the court that when her father's account was challenged, "he then made admissions that he had shaken the baby".
The court heard that during the two days of interviews, the defendant was granted compassionate police bail "in the tragic and exceptional circumstances" and in the company of officers and his solicitor, was allowed to visit Cárágh's bedside for 80 minutes.
Under questioning by police, he claimed he had been looking after his daughter when she "became suddenly ill" so in a "panic," he took steps which he thought were "perfectly reasonable in the circumstances".
The officer said he was objecting to bail because police feared that if released the accused would interfere with witnesses or would take flight given that he faces a potential custodial sentence for the "seriousness of the tragic circumstances".
During bail submissions, his solicitor conceded that while emotion had no place in such applications, "the image of the dignity that the family had at the bedside with this gravely ill child will stay with me for a long time".
He told the court there were two addresses outside of the area where the defendant could live with relatives and added that in any event, the baby's maternal grandfather "has no objection to his living in west Belfast."
The officer agreed with the suggestion there were no witnesses to how the baby was hurt and that the case would "come down" to the opinion of medical professionals.
District Judge Mervyn Bates granted bail but with conditions that the defendant live as far as possible from the area, surrender his passport, lodge £1,000 and provide two sureties of £900, not to contact certain witnesses and family member and to have no contact with his daughter.
Ordering the 23-year-old to report to police three times a week, Judge Bates told him: "One can only the seriousness of the matter and you must abide by the conditions of bail - any breach and clearly, inevitably, you will be put immediately into custody."
On Friday night, a spokesperson for the PSNI explained: "Following the court appearance of a 23-year-old man in Craigavon this morning detectives from Serious Crime Branch will be consulting with the Public Prosecution Service in relation to this case."
On Saturday morning, a district judge permitted the identities of father and daughter to be released after a reporting restriction was lifted during a bail hearing.