From time to time you can spot "privately baptised" in a church register - this indicates a home baptism for a child who was unwell and at risk of dying before it could be brought to church. There is a special service for this in the Book of Common Prayer ; following that is a set of instructions for the Minister to follow when the child is brought to church. There is as well as a service The Ministration of Baptsim to those of Riper Years, and are able to answer for themselves
In my current indexing I am finding so, so many children baptised on one day and buried the next, or in the next week. Perinatal mortality used to be high.