Can anyone recommend a private driver? I would need them for 2 people from Hallstatt to Melk.
You may want to consider using a transfer service such as Daytrip. Our experiences with them have always been positive.
Since I dont know of one, my only suggestion would be Daytrip.com. But it will cost you just shy of $400 with them.
You could take the train to Linz and then start with a transfer. That should save some $$
Or take the train the whole way.