I'd be careful of ANY animal around a young one. They all have a distant wild streak in them and even the tamest of cats, dogs or whatever you may have can lash out in jealousy or whatever emotion they may feel at the time when they are provoked. I grew up around dogs, horses, and have had tons of tame and wild cats from the woods that I have tamed (took 6 months often) and speaking strictly for the cats here, these wild cats I sort of tamed always retained a real wild streak... but they would trust me. They'd rub on me and lay on my lap, but would not for anyone else. And some of them were big and could be real nasty if they felt like it... but I know this is not the typicl tame cat, but even those retain some wild in them and you NEVER know for sure if or when they could lash out, so if they would be jealous (yes, they can get jealous) an they are angry at the baby getting attention they used to get... look out.
I don't think the life of a baby is anything to risk, so I say keep animals well away for a long time, til the children are a bit grown, maybe 2 years old or so (maybe sooner) depending on the situation ... but use caution no matter what. I've seen what angry cats and dogs can do. It isn't pretty when it's over.