Hi There,
Just read your dilemma. As you have no status with QF they won't allow you access into their lounge when flying with Hawaiin Airlines.
Nothing worse than travelling with an infant who might need a feed a nappy change and you want to do it in relative comfort. I was thinking, if you have a six hour layover. Since you have flown with Qantas in J.
Upon your arrival in Sydney could you head to the QF domestic business lounge to refreshen up grab a shower etc., Once you completed what you need to do in the lounge make your way to the Intertnational terminal to check in for your flight feeling a little more human than what you would have done.
Good luck and happy travels.