If you want an increase with gaming performance, the Bulldozer isn't recommended. I would recommend spending a little more money on an i5 processor which will give you a lot better performance upgrade than upgrading to a bulldozer. If you do decide to upgrade to an i5, you will need to buy a new motherboard because of the different socket sizes.
Hope this helps.
If you want an amd cpu, get the ones from piledriver architecture, like the FX-6300, FX-8320/8350.
You should also consider the intel side of cpus like the i5 quad cores ones like the i5-3470 and i5-3570k.
Also why not buy a new monitor with 1080p resolution support,while at it.