I would ignore her, let her be the childish one and keep her in the dark! ha she will soon realise if she gets no juicy gossip about your bay feeding through, that your not bothered by her , don't let your OH talk about favorite baby names for goodness sake, incase shes one of those.
My strange neighbour, is actually only 11 days before me , and much, much bigger, they havn't notticed my bunp at the school yet, and actually I kind of like the fact that she will be assuming I am sooo much less preg than her ! ha ha enjoy something like that