As 1 ticket/PNR ZQN-SYD-DFW-JAX is doable, as long as QF is selling you this ticket. An airline will only sell if its meets the minium connection time (MCT). If JQ220 ZQN-SYD is late it is QF's problem to get you on other flights that get you to JAX.

Would this be booked direct with QF, a real live travel agent or some random on OTA (online travel agent)?
OTA are not travel agents but just computer programmers, who take nil responsibly for problems.

As above, its a risk I would not personally take for 1:25hr connection from JQ NZ to a QF USA bound at SYD, even if on the same PNR/ticket.

Delta/Virgin Australia is another option.