You could consider another option. My concern is being a newby with a gun and shooting something lightweight, that you will hit and only wound the dog, causing a long and protracted illness, suffering and hopefully, finally death.
How about a shotgun with what we foxhunters call "ratshot". We use it to train the dogs. You pelt their butts with it and it will seriously sting, cause a permanent impression in their brains but not cause damage.
I worry since you are new to guns. A .22 will require a very accurate shot, especially if the dog is at AA distance or moving. It won't be anything like target practice.
How about a shotgun with what we foxhunters call "ratshot". We use it to train the dogs. You pelt their butts with it and it will seriously sting, cause a permanent impression in their brains but not cause damage.
I worry since you are new to guns. A .22 will require a very accurate shot, especially if the dog is at AA distance or moving. It won't be anything like target practice.