You need to get citizenship first before you apply for a passport. My husband and I are both Australian and baby has an Australian passport. She's eligible for a HK passport but I don't want her to have one just now because neither hubby nor I have one. (he was born here, but renounced Chinese nationality, so he's a HK permanent resident still, but doesn't have the 3 stars on his ID card).
My opinion is, it's probably best to use the same country passport as the person who the bub is travelling with - usually the mother - just for simplicity. You could get both passports (dual citizenship) if Canada/Australia allow that, I dunno the rules there...
It's a fairly simple process though. For Australian passport, you need to go first to apply for citizenship by descent, then when that comes back, you can go straight to get the passport (but you have to wait to get the citizenship form first).
If you're a HK resident, you need to get some kind of right of abode sticker in the foreign passport, since they don't get ID cards until they're 11...