I would head to the QF lounge, as it is near where immigration goes through and is probably the pick of the J lounges. I would then just leave enough time to either walk or catch the train to the gate. There are plenty of the wheeled bagage carts around so walking with kids is not as hard as it could be.
QF tends to be kid friendly as QF tends to have a higher proportion of children. IME.

QF lounge is also near the main group of shops, so depending on the 6 year old they may be up for a wander and look around.

The Amex lounge and PP are nothing special.

KF