I bought the OCBC Max maternity plan (mainly because I didn't want my plan to be linked to an investment-linked policy.
I got it quite late (after my 20 week scan) though you can enrol much earlier (week 13)
I also realised during the Mt Alvernia maternity tour that they partnered with AXA to offer a complimentary 6 month free personal accident plan (BandAid) that covers mummy and child. Coverage duration starts from date of enrolment (latest by 36 weeks).
I'm sourcing around for personal accident plans and integrated shield plans for my baby.
I'm concerned with illnesses.
So far, I've spoken to AIA (you will see it as part of the SG babyclub during baby fairs, also gives a free giftbox) and AXA.
AIA offers typical hospital coverage (integrated shield plans), personal accident plans (covers HFMD etc, no minimum waiting period unlike the other companies), life insurance and critical illness plans separately.
AXA has similar plans, but they also offer a add-on rider option for their integrated shield plans to cover HFMD, dengue etc.
Yet to decide.