Though anything is possible I doubt the baby's birth was registered as Judd pre the adoption laws of 1927 (and then it would be a second birth registration by the authorities). Why after all allow the baby to be baptised a Lawrence and why create more problems for yourself trying to explain to the registrar why the baby, not your own child, was being registered as a Judd by you, or registered by a mother whose name was totally different from that the baby's registered name. Or did the Judds (having allowed the baptism in another name) bluff it out with the registrar and claim the baby was their own?
When thinking about possible hypothesises to explain the scant facts you have, you need to weigh up what are the possibilities for and against each.
What is known at this stage is the baby/child was baptised in October though we don't know at what age. You have a risky/possible birth registration in the September quarter which could cover, given the 6 weeks grace to register a birth, any child born from late April until the end of September. Arthur the older child (we think) was born in April 1905 so plenty of time for the birth of another child. By October for a late April/May birth the child would be old enough to be 'adopted'. I wouldn't add complications about wet nurses if at this point it is possible not to get more complicated. That doesn't mean in the end it might have to get more complicated, but it is better to keep it simple if possible.
Regards
Valda