Does the Rds(on) of a MOSFET vary based on source-drain voltage?
The answer to your question body is "not significantly".  The answer to your question title is "yes" -- but unless you have a really truly oddball FET, or you need insane accuracy, you don't need to worry.

RDS on is a parameter of a FET that's operating at low source to drain currents.  It specifically refers to a range of voltages where the thing is acting like a resistor, and \$v_{ds} \simeq R_{DS_{on}} i_{ds}\$.  The lower your \$v_{ds}\$ compared to the threshold voltage, the better the approximation.  Your \$v_{ds}\$ is significantly lower than the threshold voltage of most FETs, so you're OK.