This is quite correct (and it is still done, e.g. at hospitals). There is, however, also another explanation, valid in some cases: the weather (and the distance). Particularly in the extreme north (but it is known to have occured elsewhere too) it happened that the weather was so bad in the winter, and the distance was too great to travel with a newly-born child (remember, baptism was within the week - and this was not just tradition, it was the law), that emergency baptisms were performed, even though there was absolutely nothing wrong with the child.
The vicar not only confirmed the baptism, in many cases the baptism was re-performed by the vicar since, according to popular belief, it didn't take properly unless performed by a clergyman. So, in some parishes you can see notations that a whole slew of children (of various ages) were baptised on the first Sunday it was possible to travel again. And the children appear to have two Christening dates.
The reason for baptising the child wasn't only that it would burn in hell if it died, it was also in great danger if alive: it could be taken - exchanged - by trolls. Trolls loved human children since they were so much more beautiful and cleverer (and didn't burst when exposed to sunlight); it was a very real fear of a newly delivered mother that her child would be exchanged for an ugly, evil, stupid troll baby (a common insult in those days were you must have been exchanged at birth).
In fact, having a heathen baby at the farm endangered the whole farm.
It must also be noted that the mother could not perform the baptism, and that as a matter of fact she wasn't even present. She was thought of as something like a half-heathen until she was churched. Churching was supposed to take place 40 days efter delivery (40 days is in many religions a very significant number), but in actual fact (proved by the many, many notations you can see in the baptismal books) it usually took place on the fourth Sunday after the delivery. Until then the woman was not considered to be part of the congregation - though not actually a heathen of course, since she was after all baptised. In the meantime the woman wasn't allowed out of doors, in fact she was supposed to stay more or less in bed, in the room (in more well-to-do farms a small separate chamber) where she had given birth. Neighbouring women came with food and helped perform her numerous tasks and chores - so it was a kind of holiday, well deserved since women were never allowed to rest normally. But in this case it was OK since she could otherwise endanger her family and the farm.
Ingela