4 hours is a little tight to clear immigration, get into Doha to sight see and back again to get the next flight.

Should you wish to clear immigration you will need to pay 100 Qatari Riyals for the visa (valid 30 days).

I know that if you have around 6 hours, then they will pay for a tour of the city as well as the visa fee. You need to go to the transfer desk upon arrival at HIA and enquire there.

I flew into DOH last week, I had a 7 hour transit and got the tour bus and guide to myself (long story... was travelling QR First & I kicked up a fuss after they said they had not started the service at the new airport, they called the guide out just for me, whilst I waited in the arrivals lounge) Had the bus and guide to myself. I visited the Museum of Islamic Art and then went to the souks before heading back to the airport.