Remember that Hobbes was writing at a time when philosophers liked to consider a "state of nature" -- the behavior of people
before organized society, government, etc., come into being.
Many of these philosophers, including John Locke (who Jefferson cribbed heavily from when writing the US Declaration of Independence), wrote as if the morals of Enlightenment-era westerners would magically naturally exist in people living in such a "state of nature", and simply took them for granted.
Hobbes pointed out that this was balderdash. Our entire conception of propriety, of right and wrong, of what is or isn't acceptable, comes not from some natural moral law engraved into our hearts or deduced in an ideal pre-society state of pure reason, but rather is inculcated into us by the culture in which we live. So Hobbes dismissed the idea that people would be respectful and helpful in the "state of nature" and pointed out that, since that stuff only comes into being later with organized society, none of it would exist at that point. Hence the war of all against all.
Which is where your desert-island analogy, and most other attempts to tear down Hobbes' state of nature, fall apart: your stranded people come in with experience of an organized culture which taught a particular set of morals and norms. One of those norms is that the adult should go hungry to let the child eat, but there is no guarantee that some natural moral law written in the adult's heart would have produced the same outcome absent years of indoctrination in a particular culture's moral system (and in fact, in actual nature we can find examples of animal species where adults will kill and even eat young of their own species).