Obviously we don't know for certain that the child is sick/contagious but as per the OP I'll assume that he is.
That being the case and with the fact that he has the ability to work from home I would say your co-worker is being massively unprofessional, he is unnessecarily exposing his coworkers to the disruption of the noise at a minimum and to potentially getting sick at worst! And frankly it's pretty mean to the child as well, I'd bet good money that the kid would be much happier/more confortable at home with his toys etc than bored out of his skull at an office!
But getting back to the point...
It's a thorny subject to try and raise - bring it up with the co-worker directly and you risk him getting defensive if he sees it as you denegrating his parenting skills or worse - denegrating the child himself (people can be a bit hypersensitive with their kids!) So to my mind your best bet is to approach it with him a little bit sideways - express concern for the child and go from there, something like:
Is [Typhoid Billy] okay? Sounds like he's really suffering with that cough, I'm sure [The Boss] wouldn't mind if you worked from home while he's ill.
Of course the putative reason you imply was behind him bringing the child in (i.e. that he was avoiding any awkwardness with asking to work from home) may well be a million miles off base but that doesn't really matter. What is important is that you have raised the issue in a way that doesn't say anything negative about him, his parenting or poor old Typhoid Billy, and you are planting the idea of him working from home in case he genuinely missed it or giving him an easy "out" if he did think it would be a good idea but had gotten locked into the weird presenteeism phenomenon that seems to infect workplaces the world over.
Of course he might not pick up on your suggestion or he might reject it out of hand, you're probably better placed to know how he would react. If you don't think it would be productive to approach him and you have a decent rapport with your boss then you could try having a slightly more frank conversation with your boss instead:
Hi [The Boss], I'm a bit concerned about [Typhoid Billy] - he sounds like he's really suffering and I'm a bit worried about potentially carrying it home to my kids or getting sick myself. I know it's not easy getting childcare for sick kids but is it worth you asking [Billy's Dad] if he could work from home?
Whether you can do this really depends on your relationship with your boss though!
NB: Something else that occurs to me is that the company's work-from-home policy might have exclusions preventing people using it for childcare purposes. It's probably unlikely given they allow kids in the office but contradictory policies do happen!