Many school districts in Tx have age policies for K/1st but once you hit 2nd grade you can just put them in. I would suggest private school for a year and just enter in 2nd grade or maybe even stay in private until 3rd (if you think she's ready). The CBEs they use are very stressful and hard to pass in the science/social studies area due to specific curriculum items. In most districts you need to get around 90% on all four tests to skip a grade if you haven't had previous instruction (vs 70% if you've previously been in the grade). You might want to ask if her previous Kinder exp qualifies her for a lower thresh-hold of passing.
http://pol.tasb.org/Policy/Search/361?filter=AdmissionsIf it's Dallas ISD (link above), I would try to nicely remind them that their policy is fuzzy. While it does mention 5 yo in 1st grade, the policy also seems to indicate that they place the child in the grade recommended by the previous private school. It seems that in any case private school for a year would likely solve the problem.
