My chihuahua is the same way, she will try and go after anything like that. Especially coyotes.
Sometimes these little dogs believe they are a lot tougher than they are. It is funny, but a single coyote usually means there are more of them around. And they would easily make a snack out of her with no problem. The cowboys around here say that a coyote is so smart that one of them will bait in
a dog, then his buddy's will close in on the dog.
And coyotes are not above attacking people either, that happened near here a couple of times last year. Them and the owls are about the most common preditor around here, but we do get the mountain lions sometimes. And brother I'm telling you they are something else with a real attitude.
State hunters have to go after them all the time after they have been attacking cattle. So even a large dog needs some supervision with a rifle out there especially at night. Wild goats, ferrel hogs, black bears, vultures, bobcats, are all out there and a wild goat or an antelope will kill a dog if it feels threatened.
Now we also have the wolves, but I don't think they cause as much trouble as it was said they do when they were first introduced. It's usually the coyotes, and the wolf gets the blame. Wolves are spooky though, they sit on a rise watching you like the Indians used to do in the old western movies .
And if you have ever seen a Mexican eagle up close and personal they remind me of the grim reaper.
All these preditors love to find stray house cats, a cat like that wouldn't last two days out there alone.
Much less my little dogs, and anyone that thinks a buzzard wouldn't kill it's prey first is wrong.