It is quite possible to take your dogs to Dubai. If you contact K9 Friends (k9 at emirates dot net dot ae) they will be able to give you the contact details of a guy called Lee who does pet import and export. He is a great guy who does a great job. He did the shipping of my dogs from Dubai to Saudi and all went well. He double checks everything to ensure all goes smoothly. He is also very reasonably priced compared to other import/export agents. I can't recommend him enough.

Dogs are accepted in Dubai - not allowed on beaches, but there is plenty of desert outside the town that you can run them on.

Hope the move goes well
Nicola