First of all will need to pay QR 100 per adult for a visa (approx 36 usd) and if you are in transit may have difficulties with the airline confirming you outbound flights.

 

Anywhere in Doha is less than a 20 usd taxi ride from the airport.

 

Unfortunately most touristy things dont open till late afternoon/ early evening. The city tour mentioned above should be available though, then go for awalk along the Corniche and spend a couple of hours in the Souq.

 

You wont be awe inspired, but it will beat the hell out of staying in the airport for 12 hours

 

 

 

"only mad dogs and englishmen go out in the midday sun"