Honestly, a dual core CPU really sucks especially with newer titles that are utilising more than just 2 cores.
I'd invest in at least a quad-core CPU based on budget, either hyperthreading or non-hyperthreading.

Also the only thing I would worry about if you're just upgrading the GPU atm, is your power supply.

That's ofc if you want something closer to 60fps+ on most/all games
What kind of budget are you looking at for a PC?