Absolutely the real deal. The pin and catch on the back are commonly referred to as a "Saddle blanket pin." The "saddle" portion may have a maker's mark on it, able to read when you clean it up. Carefully bending the pin back into its original shape and maybe some electrolysis to clean it up the best it can be. The pin was used from the early 1900's up into the 1950's. As far as rank, the badge probably was worn by a "fireman" back then, either #3 in seniority, or station house #3. If Ft. Lee FD still exists, and has a historian, then she/he would be the one to contact about more details. Cheers and congratulations on finding an intact piece of FD history! Sub
Found the Ft. Lee Fire Department History Page. According to the page, the Hook & Ladder Company #3 was formed around 1901-1906. Hope this helps!
https://www.fortleefire.org/info/history