Hi Suzie:
My mother was an RN and went to a R. Catholic hospital nursing school and was taught the same thing that anyone could baptize a baby in an emergency. Today, most Catholics have their children baptized within 2 weeks of birth.
One problem is not to baptize an Atheist, Jewish or Muslim infant, etc. I once heard a nun say, “In an emergency baptize first then check the chart. If you made a mistake keep your mouth shut.” Frankly, I don’t think a loving god would care if the infant was baptized or not.
Some Protestants faiths require that the child wait until they have reached the "age of reason." Others require early baptism. But the issue is not to accept the found date of baptism as the date of birth, it can be a guide but not a guarantee of a date close to the birth.
Regards, Jack