DHL would be the best from here to Pakistan. You can try Aramex also but they will be slower. QPost will also deliver and they are connected to Pakistan through their Express Mail Service (EMS). Cost-wise, QPost will be the cheapest.
From Pakistan to Qatar, I guess only DHL and Pakistan Post Office can bring your parcel from Pakistan. EMS service is available at all major post offices all over the country.
The major difference between DHL and QPost is that while DHL will deliver in 4 to 5 days, QPost will deliver in 10 to 12 days, say around two weeks.