You seem to be under the impression that all YouTube has to do is to look up this person's IP address and then call the police. Quite simply, it doesn't work like that at all.
Most people's IP addresses change all the time. Mine changes at least once every 24 hours, when my router goes offline for a couple of seconds to reset itself. The only thing an IP address can tell you is approximately what city or county the person is likely to be in, and which ISP they were using. YouTube would then have to contact the ISP in question and persuade them that this was a serious issue. The ISP would then have to comb through their records, and find out which of their customers was using that specific IP address at that specific time. Somebody would then have to contact the emergency services in that area.
This, of course, is all very well, assuming the person has uploaded the video from home and not from a friend's house (for example), and that the person who uploaded the video is actually the person who made the video. It also assumes that the person didn't use an anonymizer or a proxy; if they did, it will take even longer to trace them.
If it's a serious suicide note, the person would probably have committed suicide before the video had even finished uploading. And trust me, if she was serious about wanting to die, she would have succeeded first time.