You should probably not face it by adopting a dog but by slowly introducing and eventually interacting with them. Preferably trained ones. Because they can sense that uneasiness inside you and that fear so that would be a good thing to get rid of before actually owning a dog.
NO! Jumping right into to full time commitment is too big of a step and it wouldn't be fair to the dog. You have also consider how good of a dog owner YOU would be, and just how you would care for the dog's needs, not JUST your own.
You want to get over your fear .. then volunteer at an animal shelter. Get acquainted with dogs .. If your family or friends have a dog .. then go and spend some time with it. Play ball, take it for a walk .. get to know each other. Break your phobia down slowly, and you will find if you put in the effort, it will kind of melt away.
Do NOT get a dog for you to face your fear!!!! The dog will sense your fear and will become anxious. That is just a recipe for disaster! And one the dog will pay for. Have a friend who has a calm, friendly dog let you interact with it. Then do the same with another friend's dog. Just keep exposing yourself to dogs you know are safe. When you are relaxed the dog will be relaxed.
first overcome your fear. then consider becoming an alpha dog to what will be the best friend you could ever have. A cavoodle has one of the most loving sweetest natures you will get in a small dog. I have 2 now & had 1 before. The poodle in them makes them smart. They are shed free & easy to toilet train.