I would say that for the monk to kill the rabbit to eat and survive as the last choice. And i wish that the monk could find some fruit or water to eat/drink so he can survive without killing rabbit.
Of course, the monk should know the best of result of killing as he the vows holder. No matter how his pure motive, killing is killing and there is the result for it even Lord Buddha can not escape from that.
I'd like to comment on your last comment.
It depends on the motivation of the monk. No, I am not saying that he should eat the rabbit but there are exceptions because his motivation should he choose to eat it. As such, I have found a teaching that says the opposite of what you have stated. There are ways for tantric practitioners who choose to eat meat but not reap the negative karma, bless the meat and purify it at the same time. So since it is not elaborated on whether the monk is a tantric practitioner, we can't tell the motivation or compassion.
So when it is referred, so for example, a bodhisattva, and especially one who has realizations of tantra, who has realization of generation stage, oneself as deity, and especially on the top of that who has completion stage experience, clear light, illusory body, these things, then so if there is an evil being who harms a lot, who harms so many sentient beings, or teachings, holy beings like that, then if this bodhisattva, especially this great yogi, who has those Highest Tantra experiences, is responsible to destroy that evil being, to kill, in other words to split the consciousness from the body, through meditation, through wrathful actions of tantra. So if it is tantric practitioner, like that so he is responsible because of having those qualifications, one who has the bodhicitta, great compassion, where this action doesn't become dangerous to you and tantra realizations, so he is responsible, it is a vow, samaya, it is a bodhisattva vow, to do that. While you have the capacity, if you don't do that then breaking a vow.
Another example :
Buddha killed a pirate on board a ship, because the pirate was planning to sink the ship and kill the passengers, and the Buddha's compassion for the man's karmic fate was so great that he was willing to take on the act of killing, and the karmic consequences that go with it, in service of the greater good. And my understanding is that because karma is determined by intention, the Buddha's seemingly aggressively harmful act was actually beneficial, from a karmic point of view, because his intention was pure, so he escaped harmful karmic consequences from harming a sentient being -- and thus demonstrated a valid exception to the "rules."
