The details of what I'm about to say, Michael, are in my new book. (And I hope your library will buy *two* copies.)
The morality of human rights, as I glean it from the international law of human rights, holds that every born human being has inherent dignity and is inviolable. (Nota bene: I am being descriptive in saying this, not prescriptive.) No argument according to which infanticide is morally permissible is consistent with the morality of human rights. Is it reasonable to reject the morality of human rights? Because I accept the morality of human rights on theistic grounds and doubt that there are adequate secular grounds for the morality of human rights (see my recent Commonweal essay), the question whether it is reasonable to reject the morality of human rights is, for me, the question whether it is reasonable to reject my theistic grounds and all other possible religious grounds for the morality of human rights. My answer: Of course it is. It is not unreasonable to be an atheist. Singer, I take it, is an atheist--and rejects the morality of human rights.
This still doesn't quite answer your question about Singer's position on infanticide. Let me address a friendly-amended version of your question: Is it reasonable for Singer to hold that toddlers have moral status (i.e., the moral status that, say, adult human beings have) but that infants do not--in the way it would be unreasonable for one to hold that whites have moral status but nonwhites do not, or that men have a greater moral status than women, or that Catholics have moral status but Jews do not? I am inclined to think that it is unreasonable to hold that toddlers have moral status but infants do not, because I am inclined to think that there is no difference between being a toddler and being an infant that one can reasonably believe warrants the conclusion that toddlers but not infants have moral status.
Now, Boonin's argument about the moral status of human fetuses before the emergence of organized cortical brain activity, unlike Singer's argument for the permissibility of infanticide, does not constitute a rejection of the morality of human rights. Boonin accepts that infants, newborns, and even unborn children beyond a certain stage of development (namely, the emergence of organized cortical brain activity), have moral status. Nonetheless, in my book I argue that we who affirm the morality of human rights have good reason to go further than Boonin does and affirm that every human being, born and unborn, no matter what his/her stage of development, has inherent dignity and is inviolable. Boonin and I disagree, for the reason I sketched in my previous post.
Thanks to this give-and-take with you, Michael, I can now state more clearly what I have been trying to say. For me, the morality of human rights is bedrock. One can affirm the morality of human rights and yet reasonably disagree with Robby's position on the moral status of human beings at the earliest stage of their development. One cannot affirm the morality of human rights and reasonably hold that infanticide is morally permissible. Indeed, in my judgment one cannot affirm the morality of human rights and reasonably hold that, say, post-viability abortions are morally permissible.