As a Certified Vet Tech, in my 12 or so years of experience, exotics and wildlife included, it is very hard to get a job in a zoo setting. Rehab is much much easier, but most of them start as volunteers. If you want to work in a zoo setting, which is what it sounds like, start off by finding a place to volunteer. Falconry is for letting birds of prey do what they do best...hunt. No need to get an extra peice of paper, that will absolutely mean nothing to you. Bottom line...volunteer in most places it is the only way to get experience. Be aware, death is a part of life as falconers/hunters well know, and unfortunately in the veterinary field it happens to be a large part. I work in emergency medicine and euthanize close to 45-60 animals a week. If you are not ready for that, you may want to rethink your profession.
