Not clear to me if all the flights are all QF flight numbers or both AA & QF flight numbers.
Alaska is a good FFP and has good range of partners, many in OneWorld
http://www.alaskaair.com/content/mil...-overview.aspx
Otherwise AA. Do not even think about QF: a very poor program compared to AA for people in North America
Both AA & AS will have way's to keep the account alive with non flying activities.
For both AA & AS check if the fare class is eligible to earn miles. Some are not. You will not get status.