1) RQja is usually based on the part being soldered to a PCB with a certain area (perhaps double-sided, 3 x 3 cm^2), and the ambient of the PCB being at 25 C.
2) You appear to have used the 'typical' RDSON at 25 C. If the device is heating up, RDSON will increase -- at the max. 175 C TJ, RDSON will increase by nearly 100 %. You should also start with the maximum 25 C datasheet value. Thus the correct (worst case) RDSON to use in your calculations is 4mohm*2 (if you have 10 VGS), or 5.1mohm*2 (with 4.5VGS). So 17.5 A in 10.2 mohm dissipates 3.1 W. At 60 deg/W, this would exceed the max. TJ (when starting from ambient = 25). You will probably need some small amount of heatsinking.
3) Be aware that unless you are very careful with busses on your PCB, the resistance of those and/or connectors will be significant (mohm range) and will increase the overall power dissipation in your application/board -- so it may be difficult to keep the TA for the PCB & enclosure equal to the external 'ambient' temperature.
4) Don't forget to include switching losses if you are switching the FET frequently (> 10 Hz perhaps) (and it can take many amperes of gate current to switch this size device quickly). Also if your load is not DC, the correct value to use for the current is not the average value, but the RMS value.