I have always liked the idea of starting out an essay like this with putting the reader in the middle of the action. Being able to open up with the reader immersed in the action of what you are doing in your future, such as the intense work of a doctor, could be a nice way to pull the reader into the writing sample. Envision what your most busy or intense day will be when you are a doctor. What are you doing? What do the surroundings look like? Are there others around you? What is the emotional atmosphere of the room at the time? Describing all of these in vivid detail could be a good opening to your essay of what you want to be when you become older. Then, closing it could be a continuation of this scene and what you envision its resolution to be.
You should first give a brief introduction about yourself. You could mention what kind of environment you grew up in, who influence you most in your life or etc. Adding an anecdote on why you became to have a dream as doctor would help. Then at the end, state what a doctor does that appeals to you the most. If you link that with your personal life, then voila! You have your one paragraph. Remember, it's more important to be honest than to be impressive; writing from your true feelings will be more easier than creating a dramatic, unrealistic story.
In my opininion you try to put on your first paragraph what's the sense why you wanna be a doctor. What's the first thing that make you realized that you like this and you can see a good perception about this.