By definition a libertarian would be against any laws that tells employers how much they can pay workers. Or what kind of working conditions. If we're talking about what the legal definition of a child is and what kind of work they can do then we are in a more murky area. There's a subset of libertarians that use the definition of consent to say they should be able to have sex with a six year old. What I do know however is I've seen lots of libertarian videos and essays that make the argument that child sweet shop labor is the best work the families in that part of the world can get and it is actual us that's immoral for being against the sweatshop. So yes, I very much believe libertarians in this country are in favor of child factory work.