Bit rich complaining about your own screaming child isn't it? ;-)
Seriously however what would you like the mother to do with the child? It is not like the mother a) wanted an upset child and b) was intent on disturbing the ambience of you and the rest of the lounge.
What would you like the staff to do, check mum and bubs into the airport hotel so bubs can get some rest? Personally I don't agree with the children of any age in the F lounge policy which QF has and personally I think QF should ask those travelling with children of any age to use the J lounge however the policy states that CL, Platinum and PAX in F can bring children (and as many as they want) into the lounge. While that is the case the staff are powerless to do anything about it.
As for the wi-fi it is managed by Telstra and has been rubbish for a very long time.