Public schools will only pay for private placement if they feel they cannot meet a child's educational needs in the public system. At this point, it would be beneficial for you to arrange to meet with one of the heads of the special education department in your school district to discuss your concerns.
One aspect of the laws governing special education is that all children are entitled to a free, appropriate public education (also known as FAPE). The key is for you and the school district to come to an understanding about what FAPE means for your child. What can sometimes be frustrating for parents is that a free, appropriate public education must also be balanced with the least restrictive environment (LRE). This means that there needs to be the right balance between providing your daughter with the educational services, supports, and accommodations she requires to reach her academic potential and giving her access to the general education setting as much as possible.
Intuitively, it would seem that it would benefit almost all children to be in a self-contained, center-based, or other, more restrictive environment, particularly because of the low teacher to student ratio. But there are many factors to consider when determining appropriate placement. The questions of FAPE and LRE as they relate specifically to your child should be addressed.
You may wish to request that the head of the special education department also arranges to meet with you and the other members of the IEP team in order to create a new IEP that will address your child's needs in a way that is satisfactory to both you and the school. As the parent, you have the final say in all aspects of your child's education. The school cannot implement any IEP that you do not agree to and sign.