Based on existing rules/laws, your child will be born a Singapore citizen, by virtue of you & your wife's citizenship, and the fact that neither of you are PRs in Aust. And, you'll have to submit a form to the ICA (I think) for him/her before he/she turns 1(it's a pain). If you decide to obtain PR after your studies, I don't think your son can be converted to an Aust citizen by virtue of that immediately. He/she will still have to 'serve' 10 years of residency before applying for citizenship.
Obviously, if you get Aust PR, you can apply for Aust PR for your son, based on the 'dependent' rule. And once done, I believe your son (and yourself included) will have the option of converting your PR into citizenship on the 2nd anniversary of your PR approval. The same goes for your wife. However, you'll face the same quandry a lot of us face (as shown in this forum), which is that of dual citizenship (being disallowed).
Well, that's as much as I understand and have found out.
I'm in an interesting situation too. Came to Adelaide to study 9 years ago, graduated and got my Aust PR in 2003, then married a Malaysian with Aust PR. Last year, we have a son born to us, who now has Aust citizenship (& passport). So, whenever we travel now, it's passports of 3 different countries at the immigration counter. I missed the deadline to apply Sg citizenship for my son, but I'll leave it to him to apply for it (by virtue of descend) if he wants to in future. Oh, how I love if I can have dual citizenship!!
Need your advice..
I was born in SG. Born me and Wife are PR of AUST.
Decided to give birth in Aust.
1. Can my child born in Aust apply to be citizen of Aust by virtue of birth there? since both of us are PRs of Aust?
2. Once my child is a Citizen of Aust, can he/she apply to be a citizen of SG by virtue of Citizen by Descent since I am a SG Citizen and born in SG?.
3. Is it true that dual Citizen for my child will be up to 21 years?.