No, this is definitely not normal. In her condition she should not even be going to school and should be kept under close supervision, and the root of this should be found out immediately.
She most likely has no idea what it means to actually kill herself...hasn't thought it through completely, but there may be some situation in the home that is causing her to feel this way, and it also might be where she got the idea that that is the answer to a problem, no matter how big or small. I don't know if she would actually be diagnosed with actual clinical depression or not. It seems that there is something wrong with her home life that needs to be fixed, not a medical problem.
I wouldn't worry too much about the effect it has on the other children as far as bad example. Most children would just be shocked at such an attempt, which is the natural reaction they would need to have. Now if this girl actually did kill herself, whether in front of them or not, a little group therapy might be needed.
I hope that's concise enough and mostly clear for you. I hope she gets help soon!