Don’t worry. It is free of charge if your baby is a Singapore citizen. Check out this page for more info: https://www.nhgp.com.sg/our-services/general-medical-services/Pages/child-health-services.aspx Included are also his/her milestone checks when your child gets his/her vaccines. The doctor will see your child to check that she is fine. This should also be FOC.
If you don’t visit the doctor after that, it should be free for bb.