♪
The baby is due to be born at the start of the new year ♪
Literal
Year-opening [at-に] child [subject-が] will-be-born plan [copula-です] ♪
年明け literally 'year-opening' refers to the beginning of the new year, typically early January. 産まれる is the passive/intransitive counterpart of 産む 'to give birth,' used for 'to be born' without overstating agency. The ~予定です pattern is the standard way to announce a scheduled future event: 'it is planned that ~.' The ♪ music-note emoji styles the announcement as light and excited, typical of personal blog/SNS pregnancy announcements.