Victoria Palmer was born during a Season 12 episode that aired in February of 2015. This means, she would be around the age 7 by this point. Elle Graper, who plays Victoria, was 12 when this episode was filmed. Later, in "Strangers in a Strange Land", which aired in 2023, Jimmy calls Victoria a preteen, meaning the character's age has definitely jumped a few years from what it should be.
Kasey and Jimmy should not have to make atropine from scratch, the US military developed a special auto-injector pen that contains all the drugs needed for treating nerve agent exposure. All military bases and government installations would have these pens in their emergency medical kits, including NCIS headquarters as it is smack in the middle of the Washington Navy Yard.
As a medical doctor, especially one that works for the military and has bioterrorism training, Jimmy should be well aware that the standard treatment for the V-series of nerve agents is atropine. Yet he argues with Kasey over whether they should take it or not.