I usually order such gifts from: http://www.mybabygift.com.sg Their service is always fast, reliable and good. There are a couple of gift stores in Bugis Junction that offer personalised baby gifts services but I haven't actually tried them myself. Maybe you can try those if you don't want to order things online.
For baby clothes , pillows etc.. You can check "Labels of love studio " . They provide good quality clothings such as family tee or baby romper etc.. Check them out
Chubby chubby does personalised baby clothes and blankets