Welcome to the club!

I had the same problem and had to open a special deposit account to get a credit card to purchase from the internet!

You can open a deposit account with the limit of the spending you want to buy with. You have to deposit an additional 50% of that as a guarantee (don't know for what?!)

Then you can get a credit card after one week (theoretically, although it took me 4 weeks).

See what happened to me here:
http://www.qatarliving.com/node/653071