I shipped my 1968 1750 GTV from Cape Town, South Africa to Jebel Ali Port, Dubai in 2008. This is what it cost me all in. Hope this helps;
Shipping and handling (Rohlig Grindrod) - AED 8,000
Clearance Charges (local agent) - AED 3,500
Customs Duty - AED 2,500
Tasjeel and Registration Testing - AED 2,000
p.s. right hand drive is ok is the car is pre 1975, as classic cars are allowed to be right hand drive. This is the rule if your register the car through the Sharjah Classic Car Museum. The curator Mr. Al Jarwan is a gem of a guy, with lots of information and very helpful.
Dodge Durango 5.7 Crew (2012), Subaru Outback 3.0R (2009), Alfa Romeo 1750 GTV (1968)