Dammit Q, change your pic I keep thinking your berberella, lol
Nice phil chops though
I haven't read the article yet nor have I heard of Singer's arguments for it, but I can see how it would stem from his utilitarianism, or at least could. Though I doubt Singer would advocate this in any realistic case -- I mean if it were a strict choice in this case he would concede, but since there are so many other options like adoption, abortion etc.. the scenario described would never happen.
However, the pair also want the principle of killing newborns extended to healthy babies, because a mother who is unwilling to care for it outweighs an infant's right to life.
This is exactly the fallacy -- this scenario would never happen, so the point is moot. (Not to mention the numerous prudential reasons why we could never comprehend the outcomes of utilitarian calculus.)
It's an issue to tread carefully around though -- I could see a lot of people being backed into a corner when they try to give reasons why it is permissible to kill animals and not baby humans. (Not saying the two are necessarily connected, though I have seen a lot of people become backed into this corner.)