Wow that's a great package to start on! You will both be able to live off that until you find work. Don't give up hope, its much easier to find a job when you're actually in Dubai than online from another country. Hays Recruitment are good out here, much better than in the UK.
And yes, you will be fine to live together but just be careful and respect the law and customs. Don't sign up for a house together, always write that you are single on all the millions of forms you will have to fill out, no open displays of affection etc etc. We are finding Dubai to be very liberal and quite Westernised, you will love it here