I wouldn't throw away the CPU that fast. As mentioned earlier, I think your PC should be able to run the game a lot better. First question: what resolution do you get these resultst with? I think that you should get 1080P @ medium settings with a decent framerate. On this page, you'll see that your processor isn't that low in the CPU Gaming hierarchy:
http://www.tomshardware.com/reviews/gaming-cpu-review-overclock,3106-5.html
I would do some software tweaking before buying new components:
1. Update the chipset drivers (check your mainboard) and
2. flash the firmware of your mainboard if needed!
3. Check if the Ram & Video settings in your bios/efi are set correctly.
4. Check if CPU/GPU usage is being killed by other components (virusscan for example, or other intensive background tasks). Clean your OS or even do a clean install if necessary.
5. Try lowering Anti Aliasing settings a little bit (For examnple: if it's manually set in the windows driver settings to override game settings and do 16x FSAA, that's indeed going to be a FPS killer)
I'm almost sure that other issues are causing the problems here. Buying will solve the problem, but doing some tweaking might also do the trick.