Re you don't know what to ask the school for... this is what you need to ask for. Second problem is that you need to demand, not ask. You need to get seriously pushy with these people. Read through the website, understand your rights in getting this done including your right to having them pay to do one outside of their own personnel. If they know you know the law, know your rights, they will take you a lot more seriously.
http://cecp.air.org/fba/default.asp
Real issue is that she needs at minimum a Behavioral class, not mainstream classes. Ask them what type of classes they have in the building, ask her teachers if they won't tell you. If they insist they don't have one and you've done the BIP from above, then demand that they help you find a behavioral alternative school that will work for her. If there isn't one, then you need to start looking for a residential placement. And the hardest part of that can be the funding for it... but we can help you with that too.
Find a support group for you. Start with your local mental health assoc or NAMI and the hospital closest which has a psychiatric facililty. Keep asking around until you find something. The other parents will be able to tell you what is available in your area and how to get it funded. They'll tell you how they battled with your SD and how they were successful. Local on the ground support, when you can find it, will help with all the details that we cannot here.
Animal abuse is a clear sign of something psychiatric, not parenting, not psychology, don't let them put this on you. Fight back when they try to do that.
Get strong. Stay strong. Take time for yourself to relax too, but this is a battle, borrow our warrior Mom outfit!
Just a random thought... you have tried removing all food dyes from her diet, right? Do the log to see if that's an issue for her as well.