I can't comment on post-natal women who kill their kids, but I can tell you about post-natal illness/depression/going completely bonkers .. .whatever they call it these days - because I had it. Twice. After first child - without really realising what was going on and eventually 'getting better' on my own, and then off the scale bonkers after the second, who was born two years later.
I won't go into all the gory details of my post-natal period of lunacy - only to say that it was very real, and if it wasn't for the help of a lot of people, a fantastic GP who was able to tell straight away what was wrong with me, and a wonderful support system courtesy of the much maligned NHS, and I doubt I'd be here today. I also got tremendous help from a wonderful organisation here in the UK called the APNI (Association for Post Natal illness) - so much so, that after I recovered I went on to become a counsellor for them, providing telephone support for women who were experiencing the same thing. Unless you've gone through it yourself, it is very difficult to understand, so to have someone who's experienced similar is a great support. It saved me, and in turn I was able to do my bit for others.
But back to the topic of the thread. As bad as things got, I can honestly say, hand on heart, not once did it ever cross my mind, did I ever think about harming my babies. Not once. I did think seriously about running away leaving them with my mother and partner, because I felt they would be better off without me, my thinking was that warped at the time. I also thought almost constantly about topping myself - not 'if' I was going to do it, but 'how' and would sit there thinking up all the different options, eventually deciding that throwing myself off a local bridge was the way to go.
Thankfully, and with a lot of help, I recovered .... although it was getting on for another two years, before I was completely 'back to normal'. Sadly I do know of someone, a girl I went to school with - who had it so bad, she bought a can of petrol, went up onto the downs near the local golf course, poured it over herself and lit a match. Absolutely tragic, but again, she never harmed a hair of her children's heads. In all the time I was doing the phone support for APNI, I never came across any of the new mums who were having those thoughts or admitted to having them - any thoughts of harm were directed at themselves, not their children.