In Singapore, under the Guardianship of Infants Act, the father or the mother does have the power to appoint testamentary guardians. The father of an infant may by Will appoint any person to be guardian of the infant after his death. Similarly, The mother of an infant may by Will appoint any person to be guardian of the infant after her death.
This Precedent Form on Will is in Microsoft Word format and contains a special clause to appoint a guardian for the infant upon the death of the testator/testatrix.