It’s been 4 years since I taught kindergarten, but I would always introduce Work on Writing 2nd. I just loved kindergarten Work on Writing time. It was pretty much an extension of our writer’s workshop time, but with more choices. I would introduce writing options like small stapled books and making a grocery list.
I hope that helps a bit.

I introduce work on writing second and then introduce choice. One those are set, other rotations easier to add in. Just added word work this week, so up to three rotations with choice after 29 days of school. Adding listen to reading next week. Started day one with my kinders… Thrilled with progress and stamina. Hope that helps.

There is no reason to wait until December. The kids learn that writing is telling a story on paper. We started last week, week 5 for us. We are building writing stamina which means drawing pictures at this point and telling the story with words, or maybe labeling the pictures, maybe just with the beginning letter. I recommend looking at writers workshop programs for kindergarten! My kids are at 10 minutes read to self and7 minutes writing stamina. Also I introduced listen to reading so we have 3 rounds but not with choice yet.