Hello,
This is not a problem at all.
My daughter was born outside of Canada as well.
You need to download and and fill out the "Application for a citizenship certificate (adults and minors)" form.
Translate the birth certificate, make photo's of the baby and drop it off at the embassy. Follow the steps on the cic website.
Make sure you apply for urgent processing, costs a few $'s more, but you'll get the paper in 3 weeks rather than 8 months.
Once you have this paper, apply for a canadian passport for the baby, once again, urgent processing which will be faster.
The whole process will not take anymore than 2 months if you hurry.
Important fact: make sure you apply for a passport in the country of residence as well. Otherwise they might not let the baby leave with only a canadian passport. Happened a few times in Poland.
On a side note, tell your friend to mention this to the VO that issued the PR, but the status shouldn't change.
Only thing I would worry about is travelling with such a small bundle of joy, might be hard on them and the baby.
Hope this helps
Cheers