Do you need to take the Hume Highway, or are you looking for shortest possible route?

There are two other routes that are more scenic, but will take longer as the quality of the roads wont be as good as the Hume.

The first option is via Canberra, then down through Cooma and continue on to the Princes Highway east of Lakes Entrance and then follow the Princes Highway to Melbourne. This would take approximately 3 hours longer than straight down the Hume. I have relatives in both Canberra and Sale so tend to take this route if driving between Sydney and Melbourne.

The second option is to follow the Princes Highway right along the east coast from Sydney all the way to Melbourne. You would probably be looking at 2 pretty full days driving if you took this route, but would get to see some nice coastal scenery.