Dear Anonymous,
 
I'm sorry to hear that your daughter is struggling, and you have been unsatisfied with the response from her teacher. I can't make any specific recommendations as to whether your daughter should transfer schools or repeat a grade, but I can give you some information to consider.
 
First, I think that you should take advantage of the teacher and Principal's offer for an assessment. You have a right to some form of an evaluation to determine if your daughter has any learning disabilities. Your daughter has a right to a Free and Appropriate Education (FAPE), courtesy of the Individuals with Disabilities Act (IDEA). That essentially means that the school is required to try and understand and address your daughter's academic problems, so that she has access to the same education as everyone else. For instance, if she has a learning disability, they would likely provide tutoring and other services to help her manage her work. For more on this, please see the first link below.
 
As for grade retention and promotion, there are a number of issues to consider as you evaluate your options. First, you should learn all that you can about research examining the short- and long-term effects of grade retention. The National Association of School Psychologists (NASP) has published a position statement (which means that prominent members of the NASP got together, reviewed the evidence, and determined their official "position" on the issue) on grade retention. Overall, the research indicates that students who are held back/retained have worse outcomes academically and emotionally than their peers who were also candidates for retention, but who were promoted. I included two links below for more on this.
 
I can't say whether your daughter would do best in her current public school or private school, but I do think that it would be worthwhile to pursue the assessment, so you can understand her learning. I would think long and hard about grade retention. The research doesn't really support holding children back.
 
Let us know if you have any additional questions!
 
L. Compian, Ph.D.
Child Psychologist