Any advise for a Malaysian SG PR in working in Singapore but planning to give birth in Malaysia?

Since you are PR and working here, do check with your HR whether your company insurance covers delivery in Malaysia, because some policies only cover Singapore hospitals. For the private versus public question, I have a few friends who delivered in KL private hospitals and said the costs and experience were quite good compared to Singapore private, so that might be worth looking into based on your budget and which family support you have on either side of the causeway.