If the father appears on the child's birth certificate as the father, if the child lives with the father, if the mother has abandoned the child (then you may not even have to bother contacting her), or does not oppose the child leaving with you (she already indicated so in writing), I don't see a problem from this end. The father may apply for a passport for the child, and the child can travel with the father. Migration authorities only require for the child to travel with one parent.
While mother's are usually given legal custody, in this case, if the child has been living with the father, then the father has the defacto custody. If you want to legalize this, bring the issue up with the children court and request that the father be granted formal custody. The court will most likely rule favorably, as they take into consideration first what is best for the child. If the child is already living with the father, then this should just be a routine procedure.
You need to focus most of your attention on what the Canadian migration authorities will require for relocating with the child.