If you want to run the bitcoin-qt client and solo mine using cgminer you can do that you need to enable server mode and create an RPC username and password in your bitcoin.conf file. This information will be fed to cgminer to connect to your local machine to do your mining.
However I do recommend that before you attempt to solo mine that you read a couple things. First of all here is a list of pro's and con's of solo mining vs pooled mining. https://en.bitcoin.it/wiki/Pool_vs._solo_mining Secondly once you figure out what kind of hashing rates you can get from the equipment you are mining with and plug them into a Bitcoin mining calculator to see what your expected earnings are. I encourage you at this point to look at some mining pools because you can earn a much steadier amount over a longer period of time.