If you are going to retain her, it is better to do it in Kindergarten or 1st grade.
Her being the "youngest"... is that something that she herself is at conflict with within herself, or it is something that others always tell her?
She started 1st grade at 5 then turned 6. When my kids were in that grade, that was the typical age, of that grade level, and per cut-offs for entering into Kindergarten. Per my kids' class mix, most 1st graders, become 6 in 1st grade. Those that became 7, in 1st grade were the minority. Both my kids entered Kinder at 4 then turned 5. They entered 1st grade at 5 then turned 6. My kids are both late born. Both were shyer type kids, not full extroverts like some of the other kids. But they knew themselves and knew that there are just different personalities. And they have their own small group of friends. Which is normal and fine. Academically, my kids both did fine. One of my kids has a knack for math. The other does not. So we at home also tutor them. That is what my parents did when I was a kid too. As a kid, I was not good at math either. It is still not my thing.
But my concern is: why is your daughter, so focused on how young she is and being the youngest... in her class? Unless that is always harped on to her or told to her or by others... then surely she would be focused on that aspect and "compare" herself to the others in her class and be self-conscious about it. Is she a self-assured child? Or not? Maybe, in conjunction with her academic concerns, work on nurturing her sense of self. That is always important for a child to know, to learn about themselves, no matter what age. And its best done, when they are still young like this.
I work at a school. I see and know kids that were retained for various reasons. I also see and know kids that are the "oldest" in the grade and those that are youngest because they are late born. And their academic or social astuteness.... does not always reflect.... chronological age per grade. Some youngest kids are very good academically & socially, versus older kids. And visa versa. I have also seen and know some retained kids, that have actually regressed, both academically and socially. But yet, they look and are older.
And still, no matter what age/grade... no student is perfect in every single subject, across the board. All students, learn and struggle with learning things. All students have strengths or weaknesses academically. And socially. And in conjunction with that, the student hopefully learns coping skills and grows positively, versus always seeing their flaws only.
Even if your daughter was perfect in all subjects, a kiddo may still feel inadequate. For example.
It is very important, for a kid to be taught how to know themselves and to thus feel self-assured. It is a the whole child, not just one piece of them, that enables a child to deal with things in school.
There is no one solid answer to this.
You are her Mom. You have a gut instinct. Your daughter told you her feelings as well.
What does the Teacher, think?
Anyway, these are just my various thoughts.
I have no single answer for you.
Just reflections on it per my own kids and their ages and grades and how they are doing, and as a person who works in a school and sees, kids who were or were not retained.