*Resume help!* Can you opt to not have a reference for a job?

I am a recent college graduate with a biology degree. I have a decent resume, having held all of my jobs for a long time and having great references for all of them. But they are all entry level, like working at a super market or work-study's from my college. So I am now working as a veterinary assistant which would be a HUGE resume booster...however, keeping it short, the management is severely lacking professionalism and is not what I was expecting. Furthermore, the people who will be my future references seem to dislike anyone who leaves without HAVING to (i.e moving, sick relative) There are notes at our reception desk giving instructions of how to blow off companies who call for past employees. I worry that after I work there for a year or two and want to advance my career somewhere else, they won't be receptive.

So my question is, is there any professional protocol for putting a job on a resume without giving a reference for it? I want my resume to continue to shine and this job really would be a great addition to step up my resume to the next level. I feel that without it, I won't be able to find jobs that I want. Any advice?

Don't give out references unless the application specifically asks for them.