Your daughter is academically on par and better per that other Mom's comment to you.
Your hesitation is: that your child is "shy" and sensitive and the youngest and she is tall for her age.
Per my personal observations with my own kids... Who are late born, and tall, and shy/sensitive and were academically on par.
My kids, started Kinder at 4 years old and then turned 5. MOST young children, are shy or sensitive... and are in the process of, getting used to being around many other kids, both older and younger, in a group setting. That is what Kindergarten is. Along with other social and academic learning.
Both my kids and given their late born status and being shy/sensitive... BOTH did great in Kindergarten. My son J. finished Kindergarten and will be going to 1st grade in the Fall. My daughter, also went on to 1st grade after Kindergarten and did fine.
You will see... that a child progresses and matures... in many facets as they grow up. Again, both my kids are late born, and were among the youngest in their class. But that was not even a factor in how they did in school or Kindergarten. They adjusted very well. And blossomed as their time in school went on. They never had problems. And in Kindergarten or among young children, many are J. sensitive and shier because it is a normal developmental thing.
Unless your child, has "problems" and behavioral or emotional problems and which the Teacher also notices... I really don't see why she would be held back. And if she repeats Kindergarten... how will her academic growth, be addressed? She may get bored, because she already knows those things. She will not be learning 1st grade academics in Kindergarten. She will be learning Kindergarten academics, again.
Height to M., is really not a big deal.
Both my kids are tall for their ages, but they are late born. No biggie.
The issue here is: do you really think your daughter needs to be held back? Is she suffering in Kindergarten or is she immature or lacks ability to be in a classroom? She cannot go throughout school, being among younger kids. There will always be... older kids than her. Or do you want her to be the "oldest" in her class? And no matter what age or grade, there will ALWAYS be, "sensitive" kids. This is not something that will J. disappear or go away, J. because they repeat Kindergarten. But a child will mature and grow up. Even in my daughter's 4th grade class, there are sensitive kids. No biggie. They are not at a loss. They have friends. They do fine in school. There are also many sensitive Adults. That does not mean they stay in Kindergarten forever.
And there will ALWAYS be kids in class, that are older than her, or younger. Always. But a child adjusts.
And, in most schools, Kindergarten is for 5 year olds. Or those turning 6.
BUT if your child is already 6 and then repeats Kindergarten, then she will be 1st grade age.
At my kids' school, if a child enters elementary school at 6 years old, they are put into 1st grade. Unless the parent requests that their child be in Kindergarten.
You did not say how old your daughter is currently. But I assume she is 5.
AND... did your daughter's Teacher actually tell you or recommend that your daughter be held back????
I personally do not see a reason to hold your child back.
Again, your daughter is academically above par.
She is J. late born and shy/sensitive as you say. But many kids are that way. But as life goes on and they grow-up, a child learns coping skills and socialization skills. Of which the parent also guides them on. And the child matures.