Very very few airguns, if any, are going to get a .22 pellet to that velocity. Any that might lay claim to that velocity (no matter how bogus that claim may be) would cost you quite a bit more than a .22LR firearm. 600-900fps is more realistic for .22 pellets. .177 pellets can go faster, but they are smaller/lighter than the .22's. And remember that .22 airgun pellets are quite a bit lighter than .22LR rounds. .22LR run around 36-40 grains whereas .22 pellets are more like 8-16 grains.

Still, you can easily take rabbits, squirrels, birds, etc. with an air rifle. You don't need 1100-1300 fps