Actually, there are always cheaper alternatives to most things, so dont be put off having a baby. However, it may be used as a benchmark.
Prenatal gynae visits/detail scan/basic tests/vitamins : Estimate $1k and abv if you choose a private gynae. I know of people who get referrals from polyclinic, thus as a subsidised patient, they pay much lesser, but the catch is you may not see the same doctor each time and it may be a different gynae who will deliver the baby for you.
Hospital/delivery fees : Cash about $2k for normal delivery at private hospital. Again, this depends on which type of ward you choose.
After baby is born, baby will need checkups, vaccinations and doctor visits when he/she is not feeling well. Must set aside some money for this. I estimate $1k. This depends on seeing polyclinic doctor or private paediatrician.
Milk powder/diapers/wet wipes : If you breastfeed, you can save on powder. Otherwise, a 900g can of powder costs average $35 up when baby is below 6 mths old. I would imagine an estimate of $250/month up. Again, this depends on which brand of powder and diapers you choose. When baby is 4mths old, can take cereal but this shdnt be expensive. When baby is 6mths old, they can take semi solids, so buying good fishes such as threadfins can be costly.
Pre-school : there are now enrichment centres opened to baby who are just a few mths old. If you go for those, well, maybe $200/month or so? Otherwise, not really necessary until the kid reaches nursery-going age. By then, approx $250/month for normal church kindy. Otherwise, PAP classes should be $100/month or thereabout. Enrichment classes are additional.
Also, are you planning to take care of baby yourself? If not, you need to think of babysitter/infant care charges, or giving parents more allowance if they are helping you.
If there are friends or relatives who can give you hand-me-downs, it will save you quite a lot of money. Otherwise, do set aside a sum for baby cot, stroller, car seat (if your family is driving), walker, baby apparels (such as clothes, mittens etc) and baby necessities such as steriliser, milk bottles etc.