A typical argument against vegan moralists is that rabbits and other small animals are killed in the production of supermarket vegetables, so "we might just as well eat the cow". Of course this is a logic fallacy, because the cow needs food as well, so it is the better option in terms of "suffering caused". How do you call this logic fallacy, "we can't do it perfectly, so we might just as well choose the option that suits us best"?
This is a variant of appeal to perfection, which itself is a type of false dichotomy. The general form of a false dichotomy is a forced choice between only two options, "it's either A or B," when it could in fact be C. In this specific variant the choice presented is between a perfect solution or giving up entirely.
The way to defend against a false dichotomy is to identify the plausible third option, and in the case of the appeal to perfection, that option is to improve on the default, even without reaching perfection.
In the case given, the impossible "perfect" solution A kills no animals, but the "pretty good" solution C kills fewer than the default solution B (to continue as is).
It's a perfect solution fallacy, which I believe is a more specific type of the nirvana fallacy, the name (perfect solution, not nirvana) implies. It means refusing to accept a solution because it's not perfect, or because some hypothetical better solution might exist.
The situation you gave is definitely an example of that fallacy, but keep in mind there are certainly many situations where this sort of reasoning(just less extreme) is perfectly valid. For example, if you're at the airport a few minutes before your flight boards, and want a soda(you're not terribly thirsty, you just feel like having a soda), it wouldn't necessarily be a fallacy to reject the solution of buying a soda before you get on your plane because you want a free soda. Even though in most situations that might be the perfect solution fallacy because demanding free things is usually unrealistic, you know that you can get a free soda on the plane in half an hour. On the other hand, if you wouldn't even take the free soda on the plane because the only solution you will accept is a free soda exactly right when you want it, then that would again be a perfect solution fallacy.
So yea, the situation you described is a perfect solution fallacy. Just keep in mind that for something to be a perfect solution fallacy, the person has to either be expecting a perfect solution, or rejecting a solution better than the current situation because it might leave some problems unsolved.