It can be difficult to get schools to consider outside testing even with the current testing. The WISC-III was published in 1991 and WISC-IV in 2003. The 5th addition is due out soon. It is quite outdated. A school psychologist that is doing testing would know the current versions. Did the psychologist tell you they were using WISC-III before testing her?
I think you will have trouble getting it accepted. The testing retake time I believe is at least 12 months. You could also do a different IQ test.
