Yeah, the rule for Australians born overseas seem really stringent. More so than the US which is saying something
Find out about Australian visas, immigration and citizenship.
immi.homeaffairs.gov.au
Find out about Australian visas, immigration and citizenship.
immi.homeaffairs.gov.au
As Sam said - answering two questions in the first link leads to the information that you have to bring the baby to Australia and register them there. Apparently even if both parents are Australian! No residency loophole or automatic citizenship if both parents are citizens like the US
Other countries seem more reasonable - I know Indonesia (assuming father is WNI or undeclared, pre-2006) and Italy would let you just register the birth at the consulate
Yikes... sorry you have to go through this Sam