How long do you think they survived together after the disaster? Or, how long did the man’s wife survive before making her final decision? What are the clues in the text?

Cormac McCarthy purposely blurs the sense of time. The fact that the world is dead makes the passage of time redundant: almost pointless. I think the mother might have tried to exist for a few months or even a year after the apocalypse for the sake of her child. We can see glimpses of weather patterns through the book that may constitute time but that would only be speculation.