If you do actually use some sort of low pressure pumping system a liquid flow meter, like this one, might be useful. The linked meter sends a pulse after ~2.25 ml, and least for fluids like water. For more viscous fluids like laundry soap you may need to characterize it. In any case, while not extremely accurate or precise, it should be sufficient for the task at hand. There might be others even better suited, I just don't know of any off-hand.
I use one of these to automatically measure the water into my coffe pot. Doubt it would be accurate enough for just a quarter cup of high viscosity detergent.
An electric hand soap despensor would be good to check out alright!