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In this scenario, why is the reader "letting" their daughter do anything?
Presumably if she's old enough to have sex and get pregnant, she's old enough to give consent or withhold it. (If she's too young to give consent, then the sex should be forbidden and prevented based on age alone.)
How come the question is not, "You and a Palestinian are the last people on earth. Do you reproduce with each other?"
Nope, the question has to include a creepy paternalistic attitude towards a hypothetical innocent young girl under her parent's control.
Clearly incest is the desirable outcome in this "thought experiment".
The tale of Lot and his daughters.
Not like there's enough genetic diversity either way.
Also if they're only three people left on Earth the species is super duper duper doomed