Hi- just left Doha-- yes, 2 1/2 days is fine. The Souq is across the street from the Corniche. And the Pearl-- area or statue, because the statue is right there, too.
The Islamic Art Museum is walking distance of those-- on the Corniche.
Also the National Museum is maybe 15 minute walk from the Islamic Art museum (both are great!) going oposite of the Souq.
I used the metro and it was awesome-- quick, clean and by the sites-- easy to access from the airport also. Buy a metro card upon arrival and it is loaded for 5 trips for 20 Quatai Riyal.
You can easily do both museums in a day.
There is also 3-2-1 Sport museum-- take the metro.
You can buy a 99 Quatari Riyal pass (ask when buying a ticket) and it is basically 3 for the price of 2.
You can also take the metro to Mall of Qatar.
I took a pass on the Pearl area-- if you go it is a taxi or a metro then a bus.
The National Library is awesome.
Enjoy Doha-- I found it very friendly, clean, modern. People were very helpful.