You are confusing earnings on credit card spend, and flight earning.

Using a BA credit card, you will earn BA avios based on your spend and where you spend, buying flights on BA.com will give you extra depending on the credit card. A UK issued BA Amex earns 1.5 avios per £ normally and 3 avios per £ on BA.com. No idea on the US card earning if that is what you have, you would have to check.
I do not think you can book Qantas flights only on BA.com.

The actual flight you have booked you can credit to any eligible airline frequent flyer program.
Crediting a QF flight to BA will earn as per the BAEC earning table:
http://www.britishairways.com/en-gb/...-avios/flights

You could also credit the QF flight to AA, AY, CX, MH, QF, JL, RJ, QR, S7, LA, AB, IB in oneworld (did I miss any?) and EK, and possibly a few others like EI, AS, LY,...


There is also no reason you could not purchase flights on BA.com using a Delta credit card and earn Delta miles. However you can't earn Delta miles flying a BA flight.