The new airport is located East of the current airport. Here it is on WikiMapia.
It's a bit tricky to get to.
From the Corniche going S/SE, you need to to turn left to go in the direction of the Sharq and Marriot. Go past the Marriot and follow the sign directing you to Al Wakra. The new airport will be on your left.
From Al Wakra going N on Al Matar street (the main highway that connects Doha, Al Wakra and Messaieed), turn right at the roundabout before the E-Ring. The new airport will be on your right.
The new airport is located East of the current airport. Here it is on WikiMapia.
It's a bit tricky to get to.
From the Corniche going S/SE, you need to to turn left to go in the direction of the Sharq and Marriot. Go past the Marriot and follow the sign directing you to Al Wakra. The new airport will be on your left.
From Al Wakra going N on Al Matar street (the main highway that connects Doha, Al Wakra and Messaieed), turn right at the roundabout before the E-Ring. The new airport will be on your right.
Good luck!
--Jonathan