Stumped

I've been working on a rather large philosophy project concerning government enforced occupational licensure. In writing the paper I was thinking up all the arguments that could be made in support of these licenses and then shooting them each down, but one of the arguments I've come up with has been a bit too tough for me to answer to my satisfaction. I am hoping someone tomorrow might be able to take a better shot at it then I've been capable of thus far. The argument I'm trying to shoot down goes something like this:

While libertarians often argue against the paternalism, not even they would commonly take a stance against actions made in self defense. If individuals can ethically use violence in self defense, including against the non-aggressive in particular instances where their situation is such that the continuation of their lives is dependent on the initiation of force against those innocents, then this seems to leave room for a justified system of occupational licensure. For example, if two people who cannot swim have just escaped a sinking ship and are grasping a piece of timber that is only able to support one of them above the water, even a libertarian would have difficulty in condemning either person for fighting for the exclusive use of that timber. Since this is the case it could be argued that if a person knows that if he gets very sick in the future, the continuation of his life will depend on the guarantee that his doctor is skilled enough to save his life. Since he has the right to defend his life, even if it means using violence against non-aggressive persons to do so, wouldn't this give that person an ethical basis to use the government to guarantee the quality of doctors by requiring doctors to acquire licenses to perform their jobs? Even the most stalwart libertarian would likely have difficulty justifying opposition to this self-defense argument.

I can come up with some practical arguments against this, like an argument that voluntary certification processes would likely resolve the vast majority of the potential problems that the above argument is concerned with, but I'm struggling to find a solid argument based on principle that would conclusively shut that argument down. Anyone have any ideas?