I've flown to and from Tassie alot, unfortunately mostly on Jetrats.

As far as whether to go via Melb or not, you have just as much chance of missing that connection as the one in Sydney, probably more given the shorter connection time. And then you have to hope that your QF flight is also on time, something else I wouldn't guarantee.

IME, Jetstar are normally on time. I have had a run late last year where three flights in a row I took were delayed >3 hours. But outside that I don't remember any significant delays.

In short, a connection of 3 hours JQ Dom -> QF Int at Sydney should be fine. You pick up your bags, get over to the Int terminal somehow, shouldn't take more than 45 mins. Things happen though, and I wouldn't be expecting QF to do anything, best you could hope for is their next flight to HNL which is probably a couple of days later. FWIW, I'd recommend just having hand luggage if that's possible.

Just a note, there are some QF flights out of Launceston, but if your times are specific, then they may not be of any use...