7-month-old fell off our bed and I feel terrible

My youngest daughter tends to get up in the night so my wife and I take it in turns to get up with her with the other person then taking over at 7 the next morning. She was up a few times last night and, whilst my wife took over as usual, she asked me to watch her for a few minutes at approx 7.30. I apparently agreed but have no recollection of this so am presuming I did so whilst still semi-asleep. I must have gone straight back to sleep as my daughter crawled off the bed and hit the floor (from a height of around 0.5 metres and onto a carpeted floor).I’ve taken her to a&e and have been assured she’s fine but I feel like an absolute monster. My wife was, understandably furious, too.I keep thinking of how much worse it could have been and there’s a tightness in my chest. I feel like a terrible parent and I want honest opinions from people: am I genuinely awful, being too hard on myself or a little of both? via /r/Parenting https://ift.tt/30Y6lje