Of course you can. I am also just PADI Open Water. I have joined the Doha diving club because it is very sociable and friendly (and safe) and they organize dives every weekend. But you don't have to dive with them, you can go on your own.

The only other place I have ever been diving is the Cayman Islands which is amazing and Qatar is nowhere near as good. But there are quite a lot of things to see here such as turtles, rays and there are a lot of wrecks (sunken ships) that make good diving.

If you are interested, I would be very happy to introduce you to people at the club.