"the dozen" is correct and usable in written English.
You can use "the dozen" to refer to an amount of twelve units of something (items, people, etc.). Example: I brought the dozen eggs home from the store.
Dictionary
the dozen
noun
A set of twelve.
Exact(57)
By the dozen.
Import barriers were imposed by the dozen.
Catherine Deneuve bought them by the dozen.
DEATH BY THE DOZEN, by Jenn McKinlay.
The dozen workers worked around the clock.
"Scorsese talks tens to the dozen.
The dozen Diet Cokes a day?
He saw reasons by the dozen.
It had nearly-stars by the dozen.
He begins talking ninety to the dozen.
The dozen or so students didn't mind.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com