There is still no uber pickup at DOH; uber can drop off at DOH when you are returning to the airport. Your choices are either taxi or take the Metro to the first stop and get an uber there. A number of the Doha hotel threads have some discussion regarding this.
I believe the only luggage storage at DOH is a travel agency Tawfeeq Travel at the airport Metro station. Hours are limited apparently.
Luggage Storage Open?