Hamad is one of the easier Gulf airports to leave. The limit is immigration and the visa rule for your passport, not the distance.
Official taxis and the metro are both legitimate. Pick the taxi if you are tired. Pick the metro if you are curious and not hauling a suitcase across a change of lines.
Check entry before you leave airside
Open the official Qatar visa checker on airport wifi if you have any doubt. Some passports need a Hayya visa or a hotel booking that you cannot invent in the queue.
Have the onward flight and the hotel address available offline.
Get into the car or the station
Follow signs for the official taxi rank or the metro. Ignore offers made inside the terminal.
The airport metro station is in the complex. Souq Waqif is not the same line in the usual setup: expect a change at Msheireb, and read the map in front of you rather than a screenshot from last year.
Stay in one area
Souq Waqif, Msheireb and the Museum of Islamic Art are the cluster. Once you are there, walk or take short rides.
A trip to Lusail or the desert starts from the hotel with a booking, not as a spontaneous third taxi.
Back to Hamad
Leave so you are at the airport three hours before departure. The road is short. The terminal is not small, and a short road makes people late.
If you used the metro inbound and found the change annoying with bags, take a taxi back. This is not the moment to be consistent.
Taxi
The straightforward layover choice. Once you are moving, Souq Waqif is often 20–35 minutes, depending on traffic and which kerb you actually get picked up from.
Use the official rank. Agree you are going to Souq Waqif or the hotel by name, not to 'the city'.
Metro
Doha Metro serves the airport and is clean and simple if you are happy to change trains for the souq. Buy the ticket in the station.
It is a good option with cabin luggage. It is a worse option with a family and two checked bags you had to reclaim.
What not to do
Do not build a plan that needs a desert pickup an hour after you land. Immigration plus the ride into town comes first.
Do not assume visa-free entry because the person next to you walked through. Qatar's rules are nationality-specific.