The DUP needn't be concerned. There are on the face of it a lot of barriers to that. Economics is a major one. The only way that I, for example, would consider voting for a reunited Ireland is if RoI guaranteed, in the first instance, to exceed the revenue that NI receives from the UK every year in perpetuity.
Then consider for example how integrating within the RoI would affect citizens in NI. Start with healthcare. You have to pay in RoI for various hospital admissions and just to see a GP. Why in NI would I agree to start paying for something which I currently get for free in the UK?
Wikipedia on RoI: People who are not entitled to a Medical Card (i.e. 68.1% of the population) must pay fees for certain health care services. There is a €100 A&E charge for those who attend an accident and emergency department without a referral letter from a family doctor (a visit to which usually costs €45–75, though some practices offer rates as low as €25-35 for over-65s and students
[6]).
Hospital charges (for inpatients) are a flat fee of €80 per day up to a maximum of €800 in any twelve-month period, irrespective of the actual care received.