You may have seen TV ads for life insurance for babies. The one I've seen is the 'Gerber Grow-Up' plan.
I got a quick quote on their site and the rates are $36 a year for $5,000 of coverage to $360 a year for $50,000 of coverage. It is a whole life policy. Whole life policies in general are not a good buy.
But the bottom line is that you do not NEED life insurance for an infant or child. If a child passes away then you do not have to replace their income and you have no financial debts to worry about.
The only reason to even think of life insurance for a child is to take care of funeral expenses. But even then buying life insurance is not a good financial bet. Average funeral costs are $6500 in the USA and can be had for as little as $800. According to CDC mortality rates, the risk of dying before age 18 is about 1%. Given the low risk and potential costs, a premature death of a child is something that you should self insure for.