To kill another animal in order to survive would be done out of clinging to your own life. Instead, why not sit down and meditate on your hunger while realizing the impermanence of living? You could become enlightened right then and there on that island if you confronted your fear and desire instead of breaking a precept in order to stave it off. The bhikkhu Godhika slit his own throat while meditating in order to achieve Nibbana. I think there are far more important things in Buddhism than just keeping yourself alive, even if you aren't enlightened. To place compassion towards a rat over your grasping to your own body would move you ten thousand times further towards dispassion and the mind of an Arahant than giving in to killing in order to escape and go on living.
With that said, I would never imagine criticizing someone who killed an animal in this situation; to not do so would take incredible spiritual development. I'm certain that if I was in that situation, I could not get a rat into my belly fast enough. But that's because of my own clinging and grasping and I'm sure it's not what a Buddha would do.
Gain and loss, status and disgrace,
censure and praise, pleasure and pain:
these conditions among human beings are inconstant,
impermanent, subject to change.
Knowing this, the wise person, mindful,
ponders these changing conditions.
Desirable things don’t charm the mind,
undesirable ones bring no resistance.
His welcoming and rebelling are scattered,
gone to their end,
do not exist.
- Lokavipatti Sutta