The difficulty with asking opinion on this sort of thing is that people are generally very divided on horror films anyway; some people love them and aren't remotely phased by them, some people like "non-gory" horror films only (ie paranormal type thrillers/ghost type stories), and some people absolutely hate any kind of horror film - will find anything remotely scary to be "too much/sick" etc and wouldn't let a 45 year old adult watch them.
Speaking as someone who loves horror films, Saw is pretty gory. The first one isn't too bad - it's a fascinating concept and actually, when you understand the intentions/mindset behind it, it's pretty clever. The tricky thing is that the sequels get more extreme as they go on so you have to consider the possibilty of your DD wanting to watch the rest. That said, the first one works well as a stand-alone film.
Only you know what your DD can handle. I'm not for young kids watching films ridiculously beyond their range, but I can't be a hypocrite - when I was 15 I was watching 18 cert films on a frequent basis. Mind you when I was 15, the horror films at the time were the Elm Street ones, Friday 13th etc... which are classics and amazing but rather mild by today's standards. I used to watch scary stuff with my Dad and we talked about how the effects were done etc... which I loved. To this day, I have never had a single nightmare from watching a horror film. I love horror films - I prefer psychological/paranormal type thrillers myself, but I do love the horror genre of films.
Without knowing what your DD has already watched it's difficult to comment, but if she's seriously into horror then it's not like you're making a jump from a Disney cartoon to Hostel - she's already aware of what a horror film involves. What is her perferred type of horror - does she like the gory stuff? If she's already into gore then it won't be a huge jump for her, but if she's more into the psychological stuff then it might be a bit extreme for her. If she's really into her horror though and is desperate to watch it, she'll probably find a way anyway.
Age ratings can be off in my experience - it very much depends on the person watching. There are 15 year olds who can watch almost anything and 50 year olds who would be scared watching Jurassic Park! What a person considers scary/intense/horrific is extremely subjective and a person's ability to remove themselves from what is fiction varies considerably, so to have some random stranger deciding what every single person is capable of watching seems bizarre to me. I'm not saying 12 year olds should be watching an extreme 18 cert - not at all - but in my experience it's not that big a jump from a 15 to an 18 - there are some 15 cert films that I would've thought would be an 18 and some 18's that I'd have thought were a 15. It's all extremely subjective so it ultimately comes down to what your DD likes, her maturity and what she can handle.