Does anyone know which moving companies in Al Ain, Dubai  that should be contacted to transport furniture to a new home, or which shouldn't? I need help choosing a quality moving service.

I'm sure that it's realistic not to get into the scam, if you choose a moving company on a legal service aggregator of such offers. For example, the WiseMove site is like this. You can quickly find a list of offers from all the companies in the area, inquire about their discounts or bonuses, and most importantly, find honest service reviews about the movers and packers Al Ain. This really helps to save time, money and deprives you of the problems associated with moving and transporting cargo.