Yes, that pellet rifle will kill rabbits, squirrels, pigeons. As others have mentioned, make sure that you can legally and safely shoot a pellet rifle/bb gun on that specific property.
Yes, a pellet rifle is slightly safer than a 22lr, but not by much.
Another option to consider would be a Crossman Pumpmaster 760 variable pump repeating rifle. Break barrel single shot pellet rifles are more powerful than most variable pump rifles, but that's not always a good thing, and I hate being forced to single load the pellets. The new model 760 pump rifles come with a multi-shot pellet clip so you can use it as a repeating pellet rifle, OR a repeating BB gun (cock it, pump it up, fire). I hate using break barrel rifles because even though it's faster to cock it once and load a pellet, I am a mess carrying and loading each pellet one at a time, so I prefer the repeaters. Another benefit is that you can pick how powerful you want a variable pump rifle to be. My wife and I shoot ours in our basement as practice, pump them only once and it won't penetrate its way through 2 layers of cardboard backstop. Pump it 10x and it will kill a rabbit at 30yrds with ease. Almost ALL of my hunting with a BB gun/pellet rifle has been with simple BB's, never needed that much more accuracy to use pellets.