Libertarians believe that your rights should be practically unlimited to the point that they infringe on other people's rights.
You don't commonly see libertarian opposition to abortion because most of the strongest believers in life from conception are just Christian conservative Republicans.
But as a person who believes life begins at conception or at least within a trimester, I am completely opposed to anyone who states you have the right to do anything that infringes on someone's right to live. This is the epitome of a libertarian position.
Like I said, it depends on when you think living starts. Obviously it's not right when the baby comes out; that's a completely arbitrary barrier. Is it feasibility? I don't buy that either because a baby isn't feasibly when it's born... If it's not subject to constant care and protection even after birth, it will die. Plus, even before feasibility a baby has scientifically proveable cognitive functioning, a nervous system, reaction to stimuli and definitely can feel pain.
To me, those factors basically equate to life to me. A woman's right to not be burdened by basically a parasite does not outweigh the right of a living human to continue living; that's the essence of libertarianism.
Once you you agree that the baby is a living human, it's no longer a question of what the licensed Doctor says... It has rights!
I just define life before most apparently. But that is where I think people -- and legislators -- have not fully considered the issue.
And regarding "whether the doctors know better" -- again, what doctors? Are we asking abortion doctors, or doctors who primarily deliver babies? There are many, many gynos who do not perform abortions due to moral objections. Surely they know better than legislators, right? How come it's only the abortion doctors who would know better! It's not possible that their position is influenced by financial gain?