Child labor inevitably comes up when the neophyte to libertarianism wonders how order will be maintained without Daddy Government keeping everyone in line.
There are some things that regardless of your cultural distaste for them, are not immoral. "Child Labor" does not equal child slavery.
When everyone was a subsistence farmer, children helped out around the farm as soon as they were able. There's no reason this shouldn't have a parallel in the industrialized world.
However, when a society reaches a certain level of wealth, it becomes more a matter of preference whether the child works or not. In the same way, without the necessity for workers on the farm, it becomes less of a necessity to have lots of kids, so fewer people have large families. Like the rest of the free market, family size, children, and whether they work are all self-regulating in an environment of freedom. As long as the child is not being forced or being treated unethically, there is nothing to complain about.
I married a woman who grew up working in her parents' shop since she was 7. Obeying child labor laws would have kept her away from her parents, deprived her of the lifetime learning a good work ethic, impeded her from learning all she knows about jewelry, deprived her of the ability to attend a good private college almost debt-free, and kept her from becoming the person she is today.
I see child labor laws as an impediment to the moral development and fiscal prosperity of children who, in spite of not needing to work, would appreciate or enjoy the opportunity to do so at an early age.
I would also eventually do away with truancy laws so the kids incompatible with our tyrannical mass education system can spend their time building their adulthood in more productive ways.