It would be more helpful if you said which company in Dubai. Is there a housing allowance or accommodation provided? What other possible benefits? Medical, school allowance, travel, etc? That all comes into play when helping to make the decision.
Housing in Dubai has been rising rapidly again in the last few years. For a couple getting a nice 1 or 2 bedroom apartment in a good area I think you'd be looking at $3000/month plus utilities. If you want a small townhouse in the Springs or Arabian Ranches then probably budget closer to $4000+/month.
There really is no major problem living together unmarried as long as you keep a low profile about it. Technically it is illegal, but it is very common. As mentioned, the Visa for your partner is the more difficult thing to arrange if unmarried.
With the pick up in hiring at the U.S. majors I really do not see why one would want to go to the Middle East any longer. Most of the junior F.O.s are looking to get back to the USA and even many of the captains.
Typhoonpilot