Before you rule out Qatar business using miles, you need to put in a bit of work. You'll need to look segment-by-segment, starting with USA-DOH (there are around a dozen gateaway cities), and then if you find something you want, look for DOH-CPT/JNB. If you have more time than money, this is worth the investment... of course, nothing may show up, but this is how the QR game is played.

You also may be able to find the JFK-DOH on AA in business, and then connect to South Africa on QR in economy. If you book that, you'd need to keep checking to see if QR opens up anything in business, and then call AA to try to make the switch.

Note that with World Cup in Qatar in November, flights are a bit tough to find these days. You can find more details about QR using AAadvantage miles here: Qatar Airways / QR: Redeem AA Miles for Award (master thd)