There are a resonable number of CD's in Virgin in Villaggio and a few other outlets in Doha but if you are still using CD's then you are best advised to buy what you are missing when you next go home. Alternatively have them sent over by a relative or via Aramex etc.
However, you are maybe much better advised to switch over to an MP3 player like an iPod. You can then just download to your heart's content from Apple etc. A little bit expensive but you get what you want there and then.
This can mean that some complete mugs replace their entire CD collections with digital versions as they have left some key albums in storage in the UK. Not that I would do this of course but I now have two copies of all the Beatle albums!
Do not be scared about going digital and using an Ipod. I bought one for my 50th birthday and it is a very much used present. I use the Ipod in the car (hooked into the car system), in the gym and for looking at my photos on the TV via a docking station.
Get your comfort music etc now!!!!