Like world of warcraft, d3 needs a lot of ram. It depends on memory more than CPU. If you want smooth experience, you need 8GB.
For reference, my laptop has a HD8670M, it has 384 GCN cores, 64 bit memory channel. It can handle 1600 * 900 without any AA, minor AF, low physic and low spell effect.
A8 7600M has the same amount GCN cores and with a similar clock speed. If your memory set up can take advantage of the 128 bit memory channel. I think 1080p is not an issue as long as you keep physic/AF/spell effect low and turn off AA.