It didn't work for me, I'm one of those.. hmm, "un-responsive" patients, I guess. I have panic disorder though, somewhat different. I think one of the main reasons it didn't work so well for me is because my case really isn't limited to specific phobias, some times I'll go into a fit for no apparent reason at all. Not sure if that's true or not, just a theory I have as for why it didn't help me.
What has helped me, aside from the medication I take (a combination of zoloft and ativan) is finding a focus. That is, finding something that requires my full attention to really throw myself at. For me, it's been my (very small) business. Is there anything your daughter really likes to do that you would consider a productive activity? My suggestion is to encourage that, while working with a therapist/Psychiatrist/General physician/whatever. It may help her to begin silencing all the constant fears and torment, it did for me.
One thing in particular to watch out for in any anxiety disorder, is a tendency to isolate. It's very easy for someone with these disorders to become agoraphobic. Sorry for rambling so much, you've probably heard of all of this before. I would recommend encouraging group activities as well - playing with friends, youth groups, sports, anything that encourages her to be around other people more often.
That said, CBT is usually very good, patients tend to respond much better than with other forms of therapy (or even medication) and I'm just one of the odd ones. One website that has been a great resource for me is
http://www.nomorepanic.co.uk - it's a forum based in the UK, and there's a lot of great information there relating to many different forms of anxiety.
Best of luck to you, wish I could be of more help.
Dave