The OP was asking about 'earliest Qantas Haneda check in time'. Your 7:40pm flight seems to be JL51, HND to SYD. There are numerous JAL flts in all directions from HND around that time, thus the JAL counters will be open for all flts, unlike QF check in, cf QF only flight at 10:00pm (QF60), (discounting QF26 at 06:55).
Adjacent to one of the elevators on departure floor (3F), near counter 'H', there is a bench/seat area labelled 'repacking area'. Not secluded or private, but at least a place to do what you want.