Dogs are carnivores and predators. Some have a higher prey drive than others, but yeah, it not uncommon. My dogs LOVE rabbit, it's big hit around here, even my picky boy will eat whole rabbits. The only thing I'd watch for with eating wild prey is parasites. I'd just keep an eye on him.
My JRT was so fast that she regularly caught squirrels. She had a CRAZY prey drive. My current dog has fallen asleep with a friend's guinea pig (no one new it had gotten out) and made friends with cats but has killed groundhogs...go figure...she's also been ousted from her pool my my pet ducks and sits there and cries while they have fun. Some dogs would just kill the ducks but not her...so it varies from dog to dog.
One of my mom's scotties use to catch and eat sparrows. She was large for a scottie and kind of klutzy, I have no idea how she did it. My childhood scottie use to kill any wild small animal she could. Squirrels, mice, voles and once a possum. But she never hurt my pets, she even let my pet rats run all over her. Some dogs just have a higher prey drive than others.
Hitting it in the head sounds kind of strange and funny in a sick way. =P But yeah, killing and eating a rabbit is completely normal dog behavior. It also means nothing negative about the dog's nature. One of the sweetest dogs I've ever known was wonderful with other dogs and people, but an extremely efficient and skilled killer of rabbits, groundhogs, birds and other small animals.
It is kind of freaky when our domestic pets go all National Geographic all of a sudden and we see them kill (and eat or sometimes just kill) another animal. The only one of mine that has every killed anything (that I know of) is my oldest dog, Archie. I've watched him kill two full grown possums. It was quite a sight, and frankly, because I have horses and possums can carry a disease that is very debilitating to horses, I let Archie do his thing. Both times the possums were in the barn (and one was up trying to get into my horse feed), and both times the other dogs wanted to help, but they weren't big enough to kill that size animal (they're 50+ lbs to Archie's 100+ lbs). Archie is usually a very placid, easy-going fella, but he absolutely wasted no time in wasting those possums. He crushed their skulls like a nutcracker cracking a pecan. It was both gross and impressive.
Now I've had some CATS that were incredible hunters. I've walked up on them eating birds, rats, mice, moles, and snakes. And one time I found HALF of a squirrel. I picked it up by the tail (I had on gloves, though in reflection that's still kind of gross, lol) and was holding one of my barn cats (a big male) in my arms. He jumped out of my arms, grabbing the half-squirrel as he went and drug that thing away like a cheetah with an antelope! LOL!
I don't mind when my pets hunt and kill wild animals. But I do get upset to see domestic animals killing other domestic animals. I used to work at a horse farm and the owner had the nicest black lab. He was just a sweetheart. Typical lovable lab who was friendly to everyone and loved to fetch his tennis ball more than life. EXCEPT, he'd kill a cat in the blink of an eye. I didn't know this one day when I let him come in the tack room and there was a little kitten in there. He snatched that kitten up like a piece of hamburger and ran out with it. We got the kitten away from him before he killed it, but just barely. It was pretty traumatized. That same dog killed my friend's cat (she lived on the property). It was a house cat and it just slipped out the door when my friend was leaving one day. The dog was on the porch and before my friend could stop it he'd grabbed the cat, shook it, and tossed it (dead) at my friend's feet. Yikes.
Then there was the time my neighbors' *beeping* pack of dogs came onto my property (which is why I have fences and gates everywhere), drug one of my old, decrepit barn cats out from under his resting spot under a bush near the barn, and began ripping him apart while he was screaming bloody murder. I ran out there and chased the dogs off and the poor cat was still barely alive. He died within minutes. That broke my heart.
I think Winston would kill a squirrel if he ever got the chance. I don't have any on my property, but my parents do and Winston goes bonkers when he sees them. Interestingly, none of my crowd bothers cats. Not MY cats anyway. Let a strange one run through here and they'll chase and bark. I don't know what they'd do if they caught one.