Firstly, people on this forum do not work for QF or JQ and hence can only speculate as to the reasons they think may be affecting the availability you are seeing. Only people who work in the relevant yield management departments of QF and JQ can answer your question definitively and they are unlikely to do so in a public forum.
Note also that QF FF program terms and conditions state the following:
QF FF said:
13.2.3 Award Flights must be booked between 353 days and 24 hours before the scheduled departure. Award Flight bookings will not be accepted within 24 hours of scheduled departure. However, some regional and overseas locations may require booking up to 14 days or more in advance to facilitate the issuing and mailing of Award Flight tickets. Minimum booking times for departure ports are available on the Qantas Frequent Flyer website at qantas.com via a link titled "What can you book online?" Information on other ports is available by calling Qantas reservations.
Award bookings on Japan Airlines domestic itineraries can only be made two months prior to departure from 9.30am Japan time.
This in now was states that all award availability will be loaded into the systems exactly 353 days ahead. It just says that you can make award bookings up to 353 days ahead - pending availability of course.
Qantas FF seats can be booked only after the airline has loaded the availability into the systems and made it available to QF FF. In most cases, this is 353 days out for QF flights, and tends to be 330 days out for most partner airlines. For the purpose of QFF program, JQ is a partner airline. Note the specific mention that JL domestic awards are not loaded until the 2 month mark. Again this does not say they will be loaded exactly two months out, but that they won't be loaded until after the two month mark has passed.
All you can do it keep looking. Its quite possible that JQ may be loading their award seat availability only once per month. But again this is pure speculation. Perhaps the person responsible for doing that task is on leave for a few weeks and will catch up when they return. There are lots of possible explanations - none of which are likely to be verified here.
Note also that the second half of September and the beginning of October is school holiday period (the dates vary from state to state and cover about a 4 weeks period across Australia). It is also possible that JQ expects they can sell all of their seats during the school holidays so will not be making any available for awards until closer to the travel date when the yield management dept has a better feel for demand from paying customers.