Predators in My Back Yard?

I guess that is what the wild west is all about. A couple of days ago as I was taking out the recyclables and watching my little Loki sniffing around, I saw she was sniffing at something....DEAD.  Ewww! Terry was leaving for work and he commented it was a furry little animal. He had to go so it was up to me to 'clean' up the carnage. Turns out it was a poor little bunny. All that was left of it was its hind legs and its ears and face. I think a cat or a coyote got it. I had to clean up the yard of doggy waste and so i picked the poor little thing up with the pooper scooper. No I don't particularly like the idea of touching dead things directly. The dry heat did its thing and the little body was dried out even though it looked like fresh kill. In fact it could not have been there more than a day since I have a little practise of cleaning up the doggy droppings daily.
What bothers me though is that my little chihuahuas are no bigger than that little bunny was. Now I feel i have to double check the door is locked and the blinds are pulled so that whatever it was that got the bunny doesn't 'see' my little guys through the glass at night. I realize I am living in a natural setting but it does not not make the incident any less traumatic. Here's hoping the coyotes are afraid of people and will not come up when they see me or my husband around. But even my 12 pound Loki is no match for a coyote. I am not even sure she could fend off a large domestic cat. This sure does make for an argument to have a large breed dog but honestly I have already come to the conclusion I will stick with these little guys to the end but not take on any more dogs, cats, birds or any other pets. Someday I want to travel more. But I definitely don't want a predator to take my babies away before their time. Would you?