Look at each of the airline web sites. You cannot combine or transfer points-miles between each freq flyer program. Having 3 FFP account’s with Oneworld airlines is not an efficient way of collecting points-miles. AA is likely to best single FFP as QF & LAN flights will probably be able to be credited to AA, depending on ticket class and other restrictions

I doubt if you have enough miles/points get an award ticket on any airline. Time to get the credit card out for your Peru trip.