jamhind, you generally don't have to worry about the paperwork. Most professional moving companies (whether they are moving companies or relocation companies) will handle the paperwork here in Dubai.
In a nutshell:
A relocation company will do everything a moving company will do but will ALSO help you with regards to settling in. So, they might help you find a home, schools for your kids, they ,might conduct an orientation of the city for you. There are all sorts of services they might provide.
A moving company will do the move but not the housing, schools etc...
Normally, a relocation company will subcontract the moving part to a moving company.
At the same time ,a moving company may offer relocation services!
Anyway, unless you want all the additional services, you should look for a plain and simple moving company.
Any international moving company will have its standard partners in other countries.
So, for example, you book the move with CompanyX in Oz. Company X will come to your house, pack your stuff, and get it out of Oz for you by boat or plane, whichever you need. They will ALSO have a moving company here in Dubai who they normally do business with and they will have that company collect your shipment on arrival, handle all the paperwork, deliver it to your home and unpack it, on their behalf.
It is unusual when the moving company does not handle the paperwork and usually it's a matter of the mover asking them not to because the mover decides they'd rather save the money and do it themselves. Like I said, unusual, as most would MUCH rather pay the mover and have it all done for them!!
As I said earlier though, you can always choose to book the move with a mover based here in Dubai if you would like that added plus of being able to get in their faces should you need to! But, if you go with a FIDI mover, you generally don't need to get in their faces.
Also consider that the benefit of going with an Aussie mover is that the people who do the packing (the most critical controllable variable in the whole "getting my things to destination in one piece" equation) are the ones with whom you have booked the move.
If you did decide to use a FIDI mover from Oz, they will normally also use a FIDI mover to do the end bit here in Dubai. And it is your right as the client to ask who they plan to use at destination and whether they are FIDI or not.
You also have the right to specify who you want them to use at destination.
Equally, if you book the move with a company here in Dubai, you can tell them who you want them to use in Oz.
I would only advise doing that if you have good reason to use a particular company other than the one you're booking with. So for example, you book with a company here in Dubai but a friend in Oz tells you they have a good friend who has a small moving company and who will take good care of you because they're a friend so you want to use them.
Otherwise, let the company you book with, pick the other company.
If you have any specific questions, feel free to ask... my email is mercedes dot king71 at gmail dot com