First - you need to ask yourself - do you even like dogs? Do you want that kind of responsibility? It's not just a tool. It will be like
having a child. It's not just something you "shell money out for." It is a 24/7 job, AND relationship, for you.
Yes; as long as you do good work, and are respectful, and likeable, you'll have no problem getting a job in any of those fields. During the course of your learning, you will want to also build up a resume, and get some good references which will help as well.