My husband and I went through this same situation 2 years ago. My oldest daughter's birthday is also at the end of August. I was on the fence for a long time. Since you're writing to seek advice it sounds like you're on the fence also.
Factors to consider: Academics, Social skills, and emotional stability.
Academically, she was off the charts. Socially, she made friends on her own terms, slowly. In our case, we felt she wasn't emotionally ready for kindergarten. She needed more guidance on how to handle different situations. We didn't want this to effect her academically.
We thought if we held her back and she ended up being bored with school, we could always find other means to challenge her. We didn't want to chance being on the reverse end and her struggle with her school work. She's a bit of a perfectionist.
We went to kindergarten orientation and got all of the information. I knew in my gut she wasn't ready.
I am aware that as parents we cannot control everything our children do or say. However, one thing I am confident in is how my kid is being raised and what her value system should be. Many times kids are influenced by older kids. I want my kid to be "the older kid."
Kids can always be challenged. As parents, that's our job. Socially, we can teach them how to act appropriately but are they comfortable? That's developmental.
I hope this helps. xo