She won't be behind. The cutoff has been September 1st for as long as I can remember for all school districts and other states.
My birthday is September 20th and I had to wait another year as well. My son's birthday is 11/26 and we opted to put him in private school because the cutoff was December 1st.
This was a big mistake. While he was able to be in the same grade as other friends, as the years moved on he wasn't able to keep up because of his maturity level. He could do the work but was unable to focus because he was the youngest person in the class. Now, he's in his correct grade and is doing great.
Don't feel she's getting left behind because there are some parents who even wait until their kids are 6 before putting them in kindergarten. While I disagree with that concept, it works for others.
Try putting her in a preschool the year before she goes to Kindergarten. Maybe that will help. Highpointe has a great program and it makes them more than ready for Kindergarten. It's in Arlington off Matlock.