I have a little experience with this so I hope you don't mind if I answer.
You can get an Unregistered Vehicle Permit (UVP) from the RTA which will cover your entire trip, including in Vic. You will however need a safety check report, which is what the old pink slip used to be, to certify that the car is at least roadworthy. Weather or not you can get a workshop to give you that without a blue slip first I am not too sure (there is also the added uncertainty of weather it would pass or not and you would have to take it to a workshop first). I know that the UVP from the RTA covers all of Australia, except WA, maybe VicRoads or whatever your version of the RTA is called has a similar deal that will make it so you won't have to bother dealing with the RTA.