Hi Rick
Welcome to SH.
I worked aboard Canberra when she was still a liner transporting passengers from Australia and New Zealand to the UK and visa versa. This was early 1970s, so a bit later than the dates you mention. However, regulations would have been the same. When we reached Australia officials would come aboard, they were very strict. I was in charge of the Crew & Isolation Hospital. Sometimes, youngsters were admitted with chickenpox or measles, not babies, but very young. As far as I remember, they were on the parents passport, usually the mother as John said. It would be very difficult to smuggle a child aboard. Remember, it was a six week trip on most ships. All cabins had a steward, so almost impossible to hide a baby from the steward or any crew member. Gossip was rife below decks and indeed upper decks. I also looked after stowaways in my hospital. They were all caught pretty quickly. Also of course are passenger lists. I emigrated on Northern Star in 1968. All passengers were listed including babies and young children. I still have that list. Passengers, including babies not on that list would have surely been found. You may gain some information from my Northern Star thread see
https://www.shippinghistory.com/showthread.php?t=17
Good luck with your novel