How do I calculate the DC output of this specific low pass filter?
Think of your resistances and capacitances as impedences. That should make things easier when you talk about feedback loops and transfer functions.

Describe your impedence function as:

\$ Z_1 = R_8 \$ and \$Z_2 = R_9 || \frac{1}{j\omega C_1} \$

(but in the Laplace domain, \$j\omega = s\$)

So your transfer function would be:

\$ \displaystyle H = -\frac{Z_2}{Z_1} \$

Negative because it is an inverting amplifier operation.