I believe the entrance of DJ to the AUS-USA market will be a very good thing for Aussies. But I do not expect it to result in the huge fare savings being touted. Yes there will be opening specials, and some seats generally available at good discount levels. But DJ's operating costs will not be so much less than QF that they can sell fares that are consistently 1 third lower than the current QF ticket sales.
From time to time you can purchase a SYD/MEL/BNE-LAX return fare for around $1300, and at the right time of the year that can also include a few night's accommodation and a day at Disneyland. If DJ enter the trans-Pacific market, I expect we will see more availability of these low fares, but not much in the way of even lower fares.
Qantas is already able to sell their seats at a premium price compared with UA, so a once-daily flight carrying 350 seats (such as a 777-300ER) is not going to make a huge hole in QF's operations. But it will mean that 350 more people per day could potentially find cheaper fares to the USA. My expectation is that DJ's entrance to that market will help to grow the number of people flying the route rather than take much of the demand from QF. And that would be good for DJ and good for travellers. I think it would be neutral for QF.
So I believe Qantas would like to see DJ start trans-Pacific flights as it would remove some of the pressure for government approval for other airlines like SQ and EK from starting on that route, and Qantas is more concerned with SQ's and EK's ability to undermine their trans-Pacific ops than they are concerned about DJ's entrance into that market.