To the question: where would the Libertarian party draw the line with regard to the age of consent? Absolutely nowhere*¹, if not specified in the constitution. The Libertarian party doesn't want the government to enforce age discrimination at movie theaters, but the current government doesn't do that anyway - the MPAA does. The Libertarian party wants any ten year old girl to be able to buy heroin legally should she choose to do so. I don't know about their position on sex consent age, but I would assume that they would hold a similar stance. They argue that it is the guardians' responsibility to protect their children, not a politician's.

Harry Browne, the former Libertarian party presidential candidate for the years of 1996 & 2000, writes in his book "The Great Libertarian Offer":
It may be hard to believe today, but early in the 20th century a 10-year-old girl could walk into a drug store and buy a bottle of whiskey or a packet of heroin.
Despite this fact that can shock people today, crime rates were only 15% of current crime rates. The arguments for legalisation of all drugs goes along the lines of:
  • By making drugs legal, gangs would have to compete with legitimate companies in the market, and probably lose.
  • Legal drugs are cheaper, so users can afford to take drugs in a less desperate and dangerous manner. (i.e. pills instead of injection.)
  • The quality of legal drugs are more guaranteed and less potent, hence safer.
  • Harder for governments to come up with an excuse to abuse civil rights of individuals.
  • Other problems that the war on drugs can bring should go away.
They don't advocate drugs, they don't advocate overly intrusive and ineffective governments either.

*¹ - wick sez "A lot of libertarians believe that drugs, like cigarettes, should have a minimum age … "no age for drugs" is a minority libertarian belief."

I agree. I've noticed that there are different kinds of libertarians/Libertarians, at least two. I described the more extreme opinions out there, and shouldn't be thought of as representing the opinoin of all libertarians/Libertarians.