Is what the doctor did, giving his son a dose of medicine that led to his death, considered involuntary manslaughter, and are blood money and expiation obligatory upon him?

If you made a mistake by administering a large, fatal dose to your son, and it is highly probable that this dose was the cause of death, then it is considered accidental killing. You are required to perform an expiation of fasting for two consecutive months and to pay the blood money (Diyyah) to your son's heirs from the Aqilah (the male paternal relatives of the perpetrator). According to the majority of scholars, you have no right to the blood money nor to inheritance. However, if you are unsure whether the dose was the cause of death, then the default is that you are absolved, especially since the deceased suffered from chronic illnesses.