The still-air distances are (from great circle mapper):
SYD (33°56'46"S 151°10'38"E)
DFW (32°53'49"N 97°02'17"W) 7454 nm
DFW (32°53'49"N 97°02'17"W)
BNE (27°23'03"S 153°07'03"E) 7215 nm
The distances previously quoted are statute miles.
As a comparison, LAX-MEL is about 6900 nm. Given that DFW-BNE would have a lower headwind component, the air distance would be comparable, and with tailwinds, SYD-DFW would be fine for an ER as well, though I'd expect it to need full fuel and the possibility of reduced payload. You'd still get a full pax load (about 310) but reduced freight.
N