A note on sacramental ministry to sick or injured children
I understand, of course, why conscientious Catholic parents whose infant or preschool child has fallen dangerously ill or injured would seek the Church’s ministry for their child. But requests for children under the age of reason (that is, 7 years, give or take, per c. 97 § 2) to receive the Sacrament of Anointing are not appropriate (c. 1004 § 1) and requests for same should not be granted by priests regardless of the severity of the child’s condition.
Instead, the proper ecclesiastical response for a pre-school child in danger of death would be to confer on the child Confirmation (cc. 889 § 2, 891) and holy Communion (albeit in accord with cc. 913 § 2, 921) and, if desired (even if the child is not in danger of death), to celebrate the Orders for the Blessing of the Sick (Book of Blessings 376 ff., esp. 399-402). Read more about it here.
The Church has, in other words, a variety of sacramental responses to the spiritual needs of very young sick or injured children, but it is important that those responses be ecclesially appropriate under the circumstances, and not necessarily the first responses that might come to mind.