Ok I have a laptop with the same specs so I'l give you a run down on what to do. but please note it will still be a tad slow and I recommend you use a different DE just as LXDE or XFCE instead of unity.
Ok first install CCM (Compiz settings) and go to open GL and uncheck sync to vblank,
now install the kernel headers (this is for the official drivers from AMD) it should be
"sudo apt-get install linux-headers-$(uname -r)"
Ok last step, go to software sources > additional drivers and activate AMD updates or one of them, hit apply. Now reboot your system for changes to take affect, if when you login its stuck at 1024x768 and compiz wont start, hit ctrl + T and reinstall the kernel headers.
Once you do all this you can still edit some settings in the AMD control pannel which may help it even more.
I hope this is helpfull.