My birth certificate is in Malaysian. Do I have to translate it into English before submitting it with my application?

This is a bit tricky questions. ICA site mentions that your documents must be translated in English so going by it - Yes, you need an official English translation of your birth certificate to apply. You can apply for an English certificate via Jabatan Pendaftaran Negara. It will cost you RM10, and you will also need a photo of your NRIC.

However also note that first official language of Singapore is Malay. (English is de facto whereas Malay is De jure). So we have seen normally all Malay documents getting accepted without having a need to translate.