Be sure to read all the details with the Disney Professional Internships. You cannot have any tattoos, or piercing beyond 1 ear piercings, you cannot have a beard (only a mustache with respect to Walt), and you must be able to smile. Most of them are reserved for seniors or students who have graduated within one year. And be sure to bone up your resume. The Disney professional internships are extremely competitive (even more than getting into vet school!!!), so work your butt off until you qualify for it. I was unable to go to the Disney professional internship, but I have one friend who did, and she loved it.
I would suggest trying for internships at your local AZA zoo, or larger zoos such as San Diego, National Zoo, or Shedd Aquarium to help build your resume. Many zoos offer "behavior" internships, take advantage of them. Remember, Disney does not want to train you, they want a well qualified individual who already has the skills needed to fulfill the position.
Also volunteer with the zoos, even if they decline you for an internship. Networking is usually half of what is needed to be successful in the zoo world.