Progress has been quite good. I've got the core mechanics down. I'm beginning to feel that my idea is maybe a little too simple (or maybe I'm just really awesome). Most of the effort will be put into making the individual levels, so that's probably what the next few days will consist of.
Some of the things I have implemented are animation (they aren't proper baby animations though), a few models and a start of the GUI. I've also found some baby/child sounds which I might use. I've been working on a song but haven't decided if I want to do it in FL Studio or just record it straight from my digital piano (I'm not a great performer unfortunately). I've also got a very simple and very possible story arc that I can add in.

Obligatory screenshot: