Hi Kelsey199200,
I am in the same situation. Instead of doing the manual process i.e., filling the forms and sending it through FEDEx. I would suggest you to do the birth application process online. If you are in Ontario process you will be able to do 4-in-1 registration process online. This includes doing birth registration, birth certificate, CCB and SIN all at the same time. Birth registration, CCB and SIN is free of cost. Birth certificate will cost you $25 for short-form and $35 for long-form. I think you will need long-form for passport application. You can pay through credit card.
Do a Google for "Newborn Registration Service" Ontario Canada click the first link and it has all the information regarding the 4-in-1 online registration for Ontario province.
** Note that it says that to include both parents, both should be present while submitting it online.
** Doing online registration will cut down the processing time greatly. It says you can get birth certificate, SIN, CCB in 15 days once the birth gets registered.
I talked with ServiceOntario and they told me it can take between 6 to 8 weeks for birth registration. But if you show them some kind of emergency they will make some consideration.
I Hope this helps.