The option appears right as you are about to leave the doctor's house. If you're outside the doctor's house and you were never given the option, it's a bug. The only opportunity you have to turn it on is right after character creation. After that, you can turn hardcoe mode off but you can't turn it on.
After my first character I made I walked around the house for a couple minutes. Went out and did not get it. So I closed went to options could not turn it on. After second character (after I made this topic) I got the option soon after I finished making my character. What ever the problem was it seemed to have fixed itself.
Well I am off to play New Vegas on hardcoe mode