Ermen, is your flight a CX/BA code share on the same plane, I have assumed it is, if not neilmeister's comment about the least of your worries...... stands true.
Rules for the QF International F lounge state:
Next onward flight must be on a Qantas, et. al. or oneworld operated and marketed flight. #. One guest allowed and must be travelling with the member on the same flight.
Eligible oneworld Status (Emerald) Next onward flight that day must be on a oneworld operated and marketedflight.#. One guest allowed and must be travelling on a oneworldoperated and marketed flight.#
Same rules apply for the J lounge:
Eligible Qantas Members Nextonward flight must be on a Qantas,Qantas, et. al. or on a oneworld operated and marketed flight.#. One guest allowed and must be travelling with the member on the same flight.
Eligible oneworld Status (Emerald or Sapphire) Next onward flight that day must be on a oneworld operated andmarketed flight.#. One guest allowed and must be travelling on a oneworld operated and marketed flight.#
As for OW rule on when kids become guests I believe that it is up to the carrier. I know that JAL and AA children do not count if under 2, not sure about the others.
QF is under 3, so at 6 month and 3.5, I would assume you can use the F lounge, as your children should not count as a guest, this kicks in with QF when aged 4-17. May just depend on how full the lounge is the mood of the CSM at the front desk.
Good Luck