You do not need to update your child's birth details as the information will be updated upon the registration of your child's birth at ICA (Immigration & Checkpoints Authority.You may visit the informative ICA sites for local child birth https://www.ica.gov.sg/citizen/birth/citizen_birth_register) and for Overseas child birth https://www.ica.gov.sg/citizen/overseas/birth-registration/citizen_overseas_birth_childbornoverseas.