I was planning to visit Oslo, Norway with Qatar Airways with a cheap priced ticket.
But it's necessary to wait about 8hours for the transfer at Qatar International Airport. What should I do/visit in Qatar within 8hr?
First, make sure you are allowed to leave the airport with your passport/visa.
Visa on arrival is available for many countries, but costs US$28 for 30 days. But that's only certain countries, other ones are more complicated.
Wikitravel is limited, but suggests the following sites:
Personally I'd see maybe one thing, do it properly, and then go hunt out strange foods and experiences. Middle Eastern cuisine is everywhere, and in many forms — kebabs, breads, hummus, the list goes on.
Another thing that I did in Dubai, and apparently they offer in Qatar as well is dune-bashing - riding around in big Landcruisers across the desert - it was AMAZING fun! However, after my suggestion of it to a relative went bad - don't do it if you get at all carsick ;)