AA's Platimum challenge is based on completing 10,000 Q-Points in 3 months. On a AONE4 fare, you earn 1.5 Q-Points per mile flown. So that is a requirement to fly 6667 miles to earn AA Plat status.

For QF Platinum (known on the QF board as WP status), you need to earn 1400 Status Credits. SC's are dependent upon class flown and range bands.

So careful selection of which flights get posted to which account could have you earning both during the one trip. If all those flights were put to QF, you would earn 1970 SC's.

Shorter flights in F tend to be of less value to the QF program. Flights less than 2700 miles earn the same SC's in J and F and only a 50% bonus over full Y. But once you cross the 2700 mile boundary, the QF SC's add up fast on an F fare. But of course these are also the ones that are going to earn the most miles to your AA account.

For pure status attainment, you could put all the >2700 mile segments to QF, earning 1460 SC's and Platinum status. That leaves you with 13,800 miles to put to AA, earning 20,700 Q-Points, double the requirement for Plat Challenge.

So you can chose which program to put the extra flights into. Once you reach QF Plat you are getting 100% status bonus points for AA/BA and QF (not CX). Similarly, at AA Plat level you earn 100% bonus miles.

Note that once you put points into the QF program, they can only be used for award flights or upgrades on QF flights. You cannot transfer the points out to another program.