Ease and feasibility of traveling around Singapore with an infant on public transport

Recently, my husband put across an idea for us to purchase a car since we are expecting soon. His idea was that a car gives us flexibility and convenience to travel around, especially with a child. Was just wondering if it is absolutely necessary since the public transport system is adequate for us now. Is it easy and feasible to travel with a child in Singapore on the public transport? Would also like to know what are the financial considerations in purchasing a car. Thank you in advance.