I have same case as you. My son was borned (he has US passport now) before I went to landing. Canada immigration officer asked me to send application for my son (I tell them that I can not do medicine exam during my pregnecy, so they know I have a new baby). I did submit my sons application in case they doubt my case.
I already successfully did landing and got maple card for all my family members.
It only took me $100 application fee + $80 exam fee for my son. No landing fee needed for him.
I think it would be better to apply Canada Immi for your kid.
