Euthanasia (or however you want to call it) of very early premature infants already happens...

If a baby is born before a certain amount of weeks, the chance of it surviving the first few weeks or not developing with brain damage are so slim that often they are not kept alive.

Neonatology truly is a heartbreaking specialisation...

Actually... I just read through some stuff about it... and it isn't what you think.  It's... ehm... err... unique!

http://newsbusters.org/blogs/tom-blumer/2012/02/29/journal-medical-ethics-paper-after-birth-abortion-why-should-baby-live

Their argument is simple: People justify abortion through such arguments as economic strife.  Therefore, if pre-birth abortion is ethically justified in that sense, there is no ethical reason why that should be distinguished from post-birth abortion.

Exerpt from the article above:

"... An examination of 18 European registries reveals that between 2005 and 2009 only the 64% of Down's syndrome cases were diagnosed through prenatal testing. This percentage indicates that, considering only the European areas under examination, about 1700 infants were born with Down's syndrome without parents being aware of it before birth.

... to bring up such children might be an unbearable burden on the family and on society as a whole, when the state economically provides for their care. On these grounds, the fact that a fetus has the potential to become a person who will have an (at least) acceptable life is no reason for prohibiting abortion. Therefore, we argue that, when circumstances occur after birth such that they would have justified abortion, what we call after-birth abortion should be permissible.

In spite of the oxymoron in the expression, we propose to call this practice