Way to much unless you're just trying to scare the rabbit to death. You want a 22lr, 22 mag, 17hmr. Maybe a Walther p22, Ruger Wrangler.

No, Paul pretty much summed it up.

Rolando, no Sir. On rabbits, this is a case of using a nuclear bomb when a firecracker would do. Cheers and stay safe!

It depends, is the rabbit recoil sensitive? And is he an experienced shooter? I raise meat rabbits, and I can't see any scenario where I'd buy them a gun, as they would probably try to fight back.
In all honesty though no, this would be overkill to hunt rabbits, if your in rural setting and want to snipe them out of your garden then this'll work, but if your hunting them to eat id go with something way smaller, like a 22lr, 17hmr, 410 shotgun, 20Ga shotgun, or maybe even some light 12ga birdshot. But going to big you'll destroy a good portion of the meat.

NO overkill to the max a good 22lr is all you need for rabbits