Even though my course of treatments with PCa have been more extensive than your Dad's, my age is close to his. I have been going to a Psychologist/Therapist who specializes in terminal diseases the past 30-months or so ... but just on average every 4-months.
Last fall, he recommended an anti-depressant for me and my primary prescribes it. It is the first anti-depressant i have ever used - and it has been helpful.
I live alone and deal with the PCa by myself - so depression is not at all a surprise. The same may apply to your Dad. It must be depression related to have developed or appeared so quickly.
I have had dementia in my family background - and it moves very slowly even though the symptoms are similar. It's got to be some form of depression.
Peace and wellness
Rob & Gizmo