How do I go about doing a deed poll if my child is not born is Singapore?

For changing of name in Foreign Passport, you should always check with the Foreign Embassy or Consulate Office in Singapore on whether the foreign immigration authority will accept a Singapore Deed Poll prior to making an application for a Deed Poll. At a Foreign Applicant's [non-Singapore Citizen or Singapore Permanent Resident (Blue IC)] request, we may assist him or her to prepare a Deed Poll, but we do not warrant that it will be accepted for the change of name in his or her Foreign Passport by the foreign jurisdiction / authority. We have prepared Deed Polls for foreigners who wish to change their names in their Foreign Passports, and some foreign jurisdictions do recognise Singapore Deed Poll for change of name. The onus is yours to check on this issue before applying for a Deed Poll. We are unable to advise you on foreign immigration policies. As quoted from http://www.deedpoll.sg/faq Do check with the authorities or lawyers for more information.

Am I right to say that your child is a Singaporean but not born in Singapore? If that is the case, you should be able to engage a lawyer in Singapore for a deed poll. A Deed Poll can be signed in Singapore by a Singapore Citizen or a foreigner who is a Singapore Permanent Resident. A minor (person less than 21 years of age) requires either of his/her parents (i.e. father/mother) to sign the Deed Poll on his/her behalf. A Deed Poll is required for changing the name in the Identity Card at the Immigration and Checkpoints Authority (ICA) in Singapore. An adult changing the name of his/her minor child older than 1 year, can only change the name in the Identity Card of the minor child and not the Birth Certificate of the child. http://www.myfamilylawyer.com.sg/html/name_change.html