Theoretically determining Q for an inductor
There are two aspects to be considered: Determination of the actual Q value for the inductor and the influence of finite Q on filter performance. 


Q can be determined by finding the quality factor Q for a tank circuit consisting of the corresponding L and a parallel capacitor C. This capacitor must be selected with respect to the desired frequency (identical to the resulting resonant frequency). Assuming a high-Q capacitor (best quality) the resulting Q of the tank circuit is approximately equal to the inductor Q.
Knowing this Q value it is, in principle, possible to take this Q value (resp. the corresponding loss resistance) into account during design of a filter circuit. However, in this case, no standard formulas can be used. That means, you have to derive the design formulas from the circuit.  


However, the decision if the finite Q value must be taken into account (or not) must be made with respect to other uncertainties within the whole circuit (in particular, tolerances of the other parts).