We had a similar situation, although we sent our DD to a private Kindergarten at the age of 4 and then grade skipped public Kindergarten and went into 1st Grade at age 5. Our DD started reading at 3 and reads about 5+ years above grade level and is a whiz at math. These are some of the issues that we faced.
At 3, we had our DD in Montessori school, where they learned to trace everything including their letters. They were not taught the proper sequence of writing each individual letter, so the end result was pretty bad. We thought her school would work on this...we were wrong. We ended up teaching her to rewrite each letter correctly in first grade, taking one letter per day and working on it. That helped.
Her gross and fine motor skills developed last. Because she was a full year younger than her peers, her teacher in 1st Grade thought that her writing would improve as she matured. It did, but this is what we found. In 1st Grade, very little of the writing was graded, and the journal she kept was never corrected. Therefore, throughout the school year, she very consistently misspelled the same words over and over again. (We did not find that out until the end of the year when her journals were sent home.) Because she was so far ahead of everyone else, the teachers basically ignored her if favor of helping the struggling kids. (Grrr.)
When we finally had her tested at 6, the psychologist had very good suggestions. She gave her a list of 200 commonly misspelled words to work on. In addition, we developed a spelling dictionary for her to keep at her desk and add the new words that she had trouble spelling. We specifically asked her 2nd Grade teacher to read her journal and continually add new words to her dictionary, plus the teacher allowed the kids to use dictionary.com in her class. Her writing improved substantially.
I can't imagine that someone would try to hold a child back in Kindergarten only because of writing. First grade curriculum is not that much harder and they start writing more then.
One other option in lieu of a full grade skip would be to telescope by subject into the next grade. Most of the time, the telescoping is for math and reading, where the kids go to the next grade level for instruction, but then stay with their age piers for the rest of the day.
With our daughter, the school was initially going to telescope for Math and Reading, although after evaluating her they determined that a full grade skip was in her best interest. She was the top student in 1st Grade even with the grade skip.
As a parent, you need to do what is best for the child. The school should do that too.
Good luck!