First, as far as "future-proofing," you can't. Camera's sold 5 years ago do not live up to today's standards. And in 15 years, when your baby girl is in high school, the camera that you buy now for sub $600 will give you poor results compared to video standards of that time. Over the years, you will be buying new equipment, or you will be settling for very poor looking video.
As far as something that works well in low light, you have to consider that the cameras that you are looking at already have very small sensors. The smaller the sensor, the more light that will be required in order to produce a good image. They are low-end cameras, even at $600. Sony cameras in that price range, might be your best bet. But even then… I don't mean to rain on your parade with these points, but these are realities of making video.