Muma3, I pulled DS1 out of his primary school last May for exactly the same reasons - bullying which the school, despite assurances to the contrary, couldn't or wouldn't deal with.
It had become so bad that DS1 had thought about killing himself - I didn't find out about that until later. His self-esteem, never very high to start with, went through the floor and he became depressed and withdrawn. By withdrawing him from the school, he knew that we believed him and supported him fully and that is terribly important to children in this position. Your daughter will have that feeling now and you have absolutely done the right thing for her.
I can thoroughly recommend the Kidscape website mentioned below. See if you can get her on one of their Zap courses - this is for vicitims of bullying. DS1 attended one (I went too and it was pretty theraputic for me too) and was able to see that he wasn't the only child going through this, that he could and did make friends easily with the other children and that there are people out there willing to help and to believe in him.
He is now at secondary school and doing extremely well.
Your daughter is a little younger than he was (he was in Y6), so I would look into other schools in your area unless you are happy to home-educate. DS1's old school really sat up and took notice when I withdrew him (I did also inform the LEA of my reasons). During National Anti-bullying week last November, they ran a series of activities and got Kidscape involved. In fact a member of Kidscape visited the school to run a number of course and was also instrumental in drawing up a new and more effective anti-bullying policy for the school.
Your daughter probably feels you are the best mum in the world at the moment, because you have gone out on a limb to defend her, so stop thinking you have failed her or are a crap mum. You're not.