Personally, Qatar is a boring place. There's nothing really enticing place to go here. My advice to you is just stay indoors you'll be safe from rogue teenagers who'll beat you and from stupid drivers who drives like they have a date with Death.

Zoo? you have that in your country.
Beach? I bet your own country have better beach resorts.
Water theme park? I don't think sharing a pool with someone who only takes a bath once in a blue moon is a bad idea.
Museum? You'll learn more by surfing the net.