Exactly!
Libertarians can be "very much anti-abortion" (and keep in mind that anti-abortion is quite different from pro-life), but they see abortion in the "proper context" and that it's society's issue on and not government's. Therefore, libertarians are "very much anti-abortion," but, "it's the woman's right to choose."
What you say is incorrect. Does not the child have rights to life, liberty and the pursuit of happiness? If you think a libertarian believes a mother can kill a child simply because of her own inconvenience, then you just haven't learned enough about it.