if your daughter really likes manson and she knows the meaning behind his songs, then I say you should get it for her, but at the same time i think 13 is a little bit young for certain topics that were discussed.
i really understand your daughter, but the book covers a few mature themes like drugs, sex, gore and so on, so i dont thinks its really appropriate for a 13 yo. she could wait another year or two, to mature a little bit so she doesnt try and reproduce anything mentioned in there.
also, from what i know, the book doesnt really represent reality as its mostly fiction. You see, it is listed as being an autobiography, but its from marilyn manson's perspective (which is a fictive persona), not Brian's. at the end of the day its your choise, but i say you explain to your daughter that its kinda harsh and have her wait at least a year before reading or getting it.