Is it possible if the child custody to be under the father? Child is still a baby.

It is not necessary. The judge will decide based on the situation. Considerations for Custody: When deciding who to give the custody and/or the care and control/access of your child to, the Judge may also consider your wishes and those of your spouse/ex-spouse and the wishes of your child, (if old enough to express an opinion), but the Court considers the interest of the child as paramount. http://www.lawsociety.org.sg/forPublic/YoutheLaw/CustodyMaintenance.aspx You can engage a lawyer to give a detailed consultation. Here is a list for divorce lawyers: http://sg.theasianparent.com/top-10-divorce-lawyers-in-singapore-getting-the-legal-help-you-need/