Hi
With an inland application, it is advised that you don't leave Canada. Many people have had no issue re-entering after a short holiday but you are talking about leaving for several months to give birth abroad. If CIC finds out, they will cancel your inland application.
If you apply for the Certificate of Citizenship in Singapore, you can immediately apply for a limited validity Canadian passport.
The actual processing time is usually less.
Without proof of Canadian citizenship, your baby cannot get OHIP. This is why it would be important to get the Canadian passport in Singapore.
Contact OHIP. Depending on how long you are gone, you may be able to keep coverage. As far as I know, because the baby would be born outside of Canada, s/he would have to wait the 3 months.
You really should consider having the baby in Canada.