Yes taking a short hop closer to home on any oneworld airline is another option.

And ticketing LAX-DOH-DXB-DOH-DPS may have fallen over for similar reasons to the baggage issue - doubling back on yourself. Two tickets sounds like it might be the only way to have booked that particular journey. Hopefully it all works out and you hit the 600 in time. Remember also that for a tier upgrade it's 600 qpoints in a rolling 12 months (or less) rather than a fixed 12 months before your current renewal date