You don't even need an SLR or a fast lens for newborn pics. My SLR broke right before the blessed delivery day and I was stuck using my compact. Ended up being more than adequate. For these kinds of shots I like to remember I am capturing memories, not creating art. Plus I had the video mode which was great. Personally, my wife told me not to touch the camera while the baby was actually coming out - and really, who wants to see that again?
From a Canon SD1100:
If I had to do it over again, though, I would have liked a fast standard zoom on my SLR - like a Sigma 18-50 f2.8 or similar.