Honestly, fly. I took the train from Brissie to Sydney and while you get to see the countryside (and some really beautiful countryside) you get to see an awful lot of it at about 50mph (or slower). It took 14 hours. Also I thought that the service on the train was pretty poor. The staff seemed to regard customers as inconvenient and while they weren't for the most part hostile or rude, they did seem to view any requests as impositions. Also simple things like meals weren't included in the price of the first class ticket etc. and the food was pretty crap. On the whole I wouldn't bother. Even with the extra leg and seat room in first and the generally roomier carriage it is a long time to be sitting and I can imagine it would have been quite uncomfortable in regular class carriages.
If you want to do an interesting train journey in Oz, look into either the 'Ghan (North-South, Darwin-Adelaide via Alice Springs) or the India-Pacific (East-West, Perth-Sydney via Adelaide) as the service is better and the journey is more interesting, both of those are considered among the great train journeys in the world. Even if you just did Sydney to Adelaide leg climbing up over the Blue Mountains which is an overnight journey.
To note, if you do decide to do the whole thing on the train, you will have to return to Melbourne-Sydney, Sydney-Brisbane.