Leica Q has a 24.0MP Full frame (36 x 24 mm ) sized CMOS sensor and features Maestro II processor. On the other hand, Leica D-Lux Typ 109 has a 13.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor .
Leica Q's sensor provides 11MP more than Leica D-Lux Typ 109's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Below you can see the Q Typ 116 and D-Lux Typ 109 sensor size comparison.
As seen above, Leica Q has a 3.8x Larger sensor area than Leica D-Lux Typ 109. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.