OF COURSE you will earn Qpoints when travelling on oneworld partner airlines (in eligible fare classes).

This is one of the most important pillars of any airline alliance - the ability to earn status miles/recognition across the alliance. It helps foster loyalty within the alliance. Qatar could not be said to be a member of the alliance if they were (for whatever reason) the only airline that could not allow its members to earn status miles when flying across the alliance.

In fact, QR lists it first out of all the new oneworld benefits:

http://www.qatarairways.com/Privileg..._alliance.page