You can try lowering the values of the voltage divider resistors, or better yet use a regulator.
As it is you are dropping 6 V across 4700 \$\Omega\ \$ which give you
$$\frac{6~V}{4700~ \Omega} = 0.00127~A $$
That's about what the quiescent current of the opamp is going to be, so what's going to happen is that your '12 V' is going to be more like 9 V or less, and with signal the opamp will draw more current so that voltage will be even less and fluctuating. This might be why you originally had labeled it as 4.5 V for the bias, with a 1.2 mA load from the opamp you'd get around 4.5 V across the bottom resistor of the divider. Did you base the original value on a measurement or did you just calculate it incorrectly?
This may be the cause of the noise you are getting or not, either way it's the first problem you'll need to address.
You'll also need to filter the power better, 1nF capacitors would more be used for RF bypassing than ripple filtering. C5 should probably be in the hundreds of microfarads range, you can get away with lower values if your 18 V supply already has good filtering, but even then you want the capacitors to have low impedance at audio frequencies.