From what I know, airlines decline to hv ladies in their third trimester fly unless accompanied with an obstetrician's letter. However, this should be easy to obtain.
It is frankly a good idea n decision. However, she needs to get a passport for her newborn before they can fly back.
I thought of this too when we were planning for my son. But in the end, the effort and logistics did not seem worth it to me as the child may still ultimately want to be a Singapore Citizen due to his roots and his friends. The only benefit would be that he skips NS and reservist. But if he work overseas etc, he would also be exempt from reservist. So the real gain is subjective. But the logistical trauma during the last trimester as well as the post natal period is quite siong.
Ultimately wife n I decided to just keep it simple and deliver here and let him be a SC. If he decides to study abroad and henceforth work overseas, then he can make that choice for himself. Afterall, I do not see myself right now being permanently in Aust.
Just my thoughts.
Cheers