Officers released CCTV footage after 17-month-old Sophie Anderson went missing with her parents Lucy Anderson, 30, and Stuart Creaney, 22.
They had been expected to attend a mother and toddlers group but failed to show up, and now police believe the couple may have taken the child on a ferry to Stranraer.
Police and social services said they are concerned for the child's welfare.
The infant was collected as normal from premises on Scarva Street in Banbridge, Co Down, at 10:20am on Monday to be taken to the mother and toddlers group. The pair did not attend the group and it is understood they then travelled to Belfast, where they boarded the 11:45am sailing to Stranraer.
Police believe Sophie's father boarded the 7:30am sailing earlier that morning.
Police services across the UK have been alerted and are assisting the Police Service of Northern Ireland with the investigation.
Sophie is described as having dark, wavy hair and wearing a cream John Rocha top with rusty-coloured flowers, cream jeans with pink flowers and pink Doodles shoes. She may also have been wearing a yellow coat and was in a pink pushchair.
Lucy Anderson is described as approximately 5ft 5in or 5ft 6in tall with a flushed complexion, a protruding lower lip and dark, straight hair parted in the middle. She speaks with a strong Londonderry accent.