The 'four-segment on AA metal' minimum rule for AA status historically hasn't ever been enforced by AA so far. Of course, that could change anytime, so beware...
AA has a large presence and good route network to South America, though. Although in order to use it you need to connect in the US. From your posts I presume you're a Canadian citizen so you don't need a visum to enter the US. I would not recommend routing flights to South America via the US with a Yemeni passport...QR will fly from DOH to AA's main hub in DFW starting in July, so getting to most anywhere in South America on OW will be pretty easy.

QR has good product, especially in premium cabins. I like flying them. Until the new airport opens (hopefully soon), the transfer experience in DOH is subpar for economy passengers, though (bus transfers instead of jetbridges, crowding, lounges very full and far from premium).
BUT discount economy flights on QR have very bad earning rates on ALL other oneworld FFPs. If you fly cheap Y fares on QR, expect to earn no more than 25 % of mileage flown on AAdvantage, BAEC etc. In this case, weigh your options and either spring for higher fare buckets (most of the time, an "S" fare which will earn 50% on AA is just a few bucks more than the cheapest available, you can upfare to higher bucket tickets by calling them) or go with QRs program although that doesn't provide the level of benefits AAdvantage does.
Flying business class, all OW carriers including QR and MH earn full mileage plus COS bonus on AAdvantage - same as AA itself. MH business class is very nice as well. At least on their A380s, which is what I have flown a few times now on Europe-Asia.