You'll find improved configurations in the latest DOOM version.
Your XFX R9 280x is running at full speed with the latest settings. Yes, you should be able to access Doom with decent performance.
CPU should be fine. No weird settings or issues.
Athlon X4 860k running at 4.3GHz
It's unclear how demanding Doom is on CPU power, especially for a 860k. I think it shouldn't make the game unplayable, though.
I can run Star Wars Battlefront at maximum performance with 60fps, which means it shouldn't be that bad.
Good luck!
Check any recent graphics card reviews for guru3d and look at the bottom of the list—your model should appear there.