Nobody we have met in the injury prevention field recommends taking an infant of less than 12 months in a bicycle child seat, trailer, sidecar or any other carrier. And we do not either. That statement explains why you will not find a child helmet on the market sized for a tiny tot. You certainly do not want to ride with a bare-headed child, and in some places it is illegal. In fact, several states have laws against taking children under one year of age on a bicycle, even with a helmet.
Parents love their babies and love their bicycles, so it is natural to want to put the two together.
That thought occurs to every bicycling parent, generally before the child is born. We see messages on the Internet indicating that some parents do put their children in baby seats of one design or another and take them along on trailers starting as young as five weeks. Others use a baby backpack. At slightly older ages, people use front or rear-mounted child seats. Each has its advantages and disadvantages.