Sure, they have laws against it. It doesn't mean they are enforced or even enforcable (just think of speeding in this country, loads of people do it on a regular basis and don't get caught). The kids want to work, and people want to employ them. Also, as it's illegal they'll hardly appear on any payrolls, so I doubt a legal minimum wage will have any effect on their earnings. Just google child labour in China, it comes up with loads of information on it.
So you can't afford ethics, but you're ok with a child most likely forced to live away from their family, barely able to afford to feed or clothe themselves, sleeping on a concrete floor, forced to work long hours with no chance to play, probably beaten, no healthcare, all for a pittance. And if they didn't have that job, what other work would they be doing??!
For baby clothes you're probably better off sticking to well known clothes brands over here, such as M&S or Next, as they employ the "good" factories to make their clothing, rather than the "squalid" ones.
I'm not claiming to be squeaky clean myself, far from it, but at least acknowledging this sort of thing does go on, and trying to do a little about it, is much better than burying your head in the sand and pretending it doesn't happen at all.