When Walt and Donna are in his bedroom, he leans his rifle against the wall near the door. In the next scene, the rifle falls and goes off, but it's right next to the bed and facing the door.
The rifle Cady uses is an antique Henry repeating rifle given to her by Jacob Nighthorse who said it was used by one of his ancestors. The Henry was one of the first commercially successful repeating rifles to be made, it was eventually succeeded by the widely known Winchester Model 1866. If so that would mean the rifle would be chambered for the .44 Henry, a short rimfire cartridge. The cartridges Cady loads into the rifle are centerfire and way too long to be a .44 Henry. In fact close examination of the ammo box shows them to be .44-40 WCF cartridges, which the Henry rifle was never chambered in; in fact there aren't even any modern replicas of the Henry chambered for that cartridge, the only additional cartridges modern replicas are offered in are: .38 Special, .357 Magnum, .44 Special, .44 Magnum, .45 Colt, .30-30 Winchester and .45-70 Government.
After Cady is shown loading the rifle, she is never shown actually chambering a round but she gets a round off anyway. After that shot, she does chamber another round, but in the ensuing close-up the hammer of the rifle is shown in the un-cocked position. She would not have been able to fire without cocking the hammer manually or cycling the action again.