Stay in Melbourne. I would suggest that the Yongala is too much of a logistical hassle given your timeframe.
1. You have to get to Townsville. There is no daily direct flight from Melbourne, it will take half a day to get there.
2. You then have to decide between Adrenalin Dive who operate out of Townsville - but who regularly cancel the trip due to weather; or Yongala Dive who operate out of Alva Beach 2 hours drive south of Townsville, who are more reliable, but how do you plan to get to Alva?
3. Given the no fly time after diving...
Yongala is awesome, but not the most practical destination for a day if you're starting out in Melbourne. You'd spend the best part of a day getting there, one day of diving, and the best part of a day getting back to Melbourne afterwards. So it's really a 3 day trip for 1 day of diving.