The phrase "mere dozen" means a small and insignificant number. It refers to just twelve of something, which is considered to be a relatively small amount. Full definition
Once there were mere dozens of minerals in the universe, but today our planet has more than 4,400 known mineral species. (scientificamerican.com)
In the fourth edition of Webster's — among the timeless explorers, artists, inventors and statesmen — are a mere dozen 20th - century sports figures. (si.com)
So requiring someone to build a track record as a responsible adult for a mere dozen years (two Senate terms) before giving them that authority seems prudent. (politics.stackexchange.com)