Christopher O'Neill, 25, was first charged with causing grievous bodily harm to Cárágh Walsh in February 2014.
However, within hours of Mr O'Neill appearing in court, Cárágh died.
Mr O'Neill, from Whiterock Road, was then charged with manslaughter, but in July, a senior prosecutor ordered a new post mortem report.
A preliminary enquiry committing Mr O'Neill to the Crown Court to stand trial for his daughter's murder, has been adjourned because of a defence application.
A defence solicitor said he had only received "voluminous papers" in the last few days, including what he described as "quite complex" medical evidence and asked the deputy district judge to adjourn the case for two weeks.
A prosecuting lawyer said she had no objection and releasing Mr O'Neill on continuing bail, the judge told him to come back on 11 September.
A Belfast man has been charged with murdering his three-month-old daughter on 7 February 2014.