Absolutely - what Karen said. And don't worry - most perspective employers won't call for a reference if you ask them not to, since they know it could jeopardize your current job. You shouldn't feel that you are going behind your present employer's back, and ya gotta do what ya gotta do!. If this present vet doesn't see you as any more accomplished than an unregistered tech, then obviously you are in a position that is going nowhere.

Go for it - and good luck!