In some denominations, if it was believed an infant was in immediate danger of dying, a family member could baptize the child in place of a minister or a priest. There may be a notation regarding this emergency baptism in the church records. Obviously not all children who are baptized under emergency situations die.
While these types of baptisms are not common, they are not unheard of either and the church record may make a note regarding the unusual nature of the baptism.
My wife's great-great-grandfather baptized his granddaughter in the early 1900s when it was believed she was near death and would not survive until the pastor could be summoned.