Truly, having dogs around gets rid of rabbits, feral cats, deer, bobcat, fishers, voles, moles...etc. You don't have to allow the dogs to kill them. Helloooo! Rabies and all kinds of disease could be transferred. It takes a few months but works just fine! I have all of the above and more. That and freezing temperatures at night any night of the year. I just went with a greenhouse and solves most of those problems.
I've shot one animal one time at 100 yards with a 22, it was a rabbit. It screamed! I'll never forget it. Made myself eat the poor thing. I have no problem with hunting and killing done correctly and humanely. I love my meat-sigh-but it'll be vegetarianism for me until I get hungry enough to kill. Lots of meat around here!
This area is full of squirrels (I love them!!), rabbits, rodents, feral cats not to mention lots of coyote, bobcat and cougar. I've two dogs I don't allow freedom to roam. My cats forever and always will be indoor cats. Yup, I have to exercise to exercise my dogs. Oh well! I've got two horses as well and I have to exercise them or be a heartless, self-centered and overweight person. This is my first garden here and it is a tough place. The greenhouses solved 90% of these problems. Having dogs, just having them here, pooping, peeing and occasionally barking has scared away most of these animals.
The point is, if you kill one, there are thousands waiting in line to fill in the niche. They do belong and it is up to us to figure out how to live together. That is why we have this so-called intelligence we think makes us so special. Killing should only be done for food. Period. Period!! I've made it happen and most of my life I've been a single parent with all of the responsibilities and work. It is not tough. Killing and pesticides are a last, last resort. They only make more trouble.
Think of it this way; you are training your environment (including your animals, varmints) to live in harmony with you. You start killing them and then you have to teach the new guys the 'rules' all over again. You allow your dogs to start killing and the next thing you know is they'll kill your neighbor's cats, little yappy dogs or bite kids. You don't need that heartache nor the expense!
Relax! If you are going to be a gardener then you should know you can't control anything!!! Orchestrating harmony is vastly superior, humility and education is a must! We are not more important nor more special than any other form of life. Asking questions on this site, studying, researching, going to school are the best ways to show we humans have something going for us. Kudos to you!!