There is no charge for QFF membership outside of Australia. However, one of the rules is that only flights taken after you join QFF can be credited. So while QFF does allow retroactive credit, it must be for flights after you have already joined. Almost all airline FF plans have a similar restriction ... so what FF plans are you and your family already a member of? BTW, this BA requirement of 4 segments and strict enforcement of this requirement (alone amongst OW airlines) is well documented on FT so it should not have come as a surprise.

The QFF rules are at http://www.qantas.com.au/fflyer/dyn/program/terms#jump9

"9.1.2 A Member may earn Points only in relation to acquiring eligible goods or services or other eligible transactions made after the Member's enrolment date"

Edit to add: you cannot double-dip. If these flights were credited to BAEC and the miles posted for the flights, you cannot claim the same flights in a 2nd OW plan; and BA will not reverse flight credits after about a week. So you are stuck with BA miles and your BA Blue status. There is no way around this except by having BAEC make an exception to the rules for you. They will do this if you are VP of a Fortune 500 company, otherwise they generally do not.