only sub domains of the .qa name server where affected (qnb.com.qa, moi.gov.qa, etc..) but all .qa domain names like qp.qa are still working fine, which means that they managed to make the .qa domain name accept wrong replies for dns queries he sends. It will take approximately 24 hours for the correct A records to be propagate again..
And yes DNSSEC should prevent these types of attacks because the answers are digitally signed which provides authentication to queries making sure they are coming from the correct server.