Yes rpatton3, you can. There are several schemes for importing vehicles to Australia. You would be able to bring your car with you as a "personal import" if you have owned it for more than a year, but it won't get registered LHD unless it is 30yo (I can only speak for the state of NSW). You will have to have it converted to RHD if its a later model and have any required mods done to comply with ADR rules.
I'm not sure what you need to migrate here, but once you're here you have to give us all a drive of your cobra
...and this is about as far away from your family you can get.
You will get used to the sharks, crocs and snakes after a while.
Mike