There is a chap called Asif Rehman in Abu Dhabi, he does lots of removals for lots of people.
This link gives you all you need to know & the phone details are still correct.
Good luck!
http://www.expatwoman.com/forum/topic197223-furniture-pick-up-within-ad-forum22.aspx
I am moving in February to a different apartment not far from my current place. I would appreciate some advice on good companies that are not too expensive.:)