For bb’s first visit to PD, do i need to bring Birth cert along?

Yes, baby's birth cert is like an IC of sorts so for registration purposes, do bring it. This also reminds me of a time when my Indonesian baby cousin was visiting Singapore and she fell sick and needed to see the doctor. Obviously her mother does not have her birth cert on hand so the clinic accepted the baby's passport for registration instead.

I bring all their health booklets, CDA card, birth certs at all their visits. I do not want to blame myself for leaving out one item and having to run back to get. I normally put all these important items in a file so I can just grab and go for emergency case.

Yes you will need to for registration purpose. You will also need to bring your baby's health booklet along for every visit to the PD. It has baby's medical records and history so do bring it along for each visit to the doctor.