if you already have an AR-15 in 5.56mm/.223 Rem. i would recommend/suggest you buy a dedicated .22 LR upper, that way you have enough firepower for small game and large game and in an emergency even a bear, if you plan on being in bear country.
have you given thought about the following along with what rifle "...and live for several months on what the land can provide." better obtain the knowledge of what plants you will need to find that are edible to live a healthy life, you can not eat only meat for "several months" unless you go full 1820's style Mountain Men, after killing a Buffalo, Elk or Deer they ate the undigested plant mater in the stomach, some ate the liver raw also using the bile to flavor the stomach contents etc.