writing job/internship references question

I am currently doing an unpaid internship which I enjoy, but recently, I found another job listing for a research assistant. Its temporary with benefits of pay & referrals to other writers. Would it be wise to apply for this while I am still interning (my internship runs out in Dec.)? This job listing requires references. Would it also be smart to add the editors I work under at my current internship as my references, with or without their permission? Thanks.