What is a pipette?
Others have mentioned that a glass tube and sticking your thumb on the end is very easy, i agree. but i'll add a little extra for a conventional pipette
A long narrow glass tube with rubber bulb at the end, which when air is expelled by pinching the rubber end, and when the glass tip is placed in liquid, and the pressure on the rubber is released. then suction drags the liquid into the glass tube and smaller pressure can release a drop of liquid at a time.
Glass blowing was common in medium to large towns and cities across Medieval Europe, and they would be capable of making a small internal diameter tube glass rod, it may have fairly thick walls of glass but its very doable.
The most likely the way it would be done would be to place a tapered steel rod into a blob of molten glass and then shape the glass around the rod, then as the glass cooled, carefully extract the rod while the glass was hard enough not to deform but molten enough to not stop the rod being removed. it being a tapered rod would make this process slightly easier.
and while rubber in the send of the bulb was not really known, rubber was, so its plausible that it could be done, it could be made out of leather, water skins were common place in medieval times, and they were capable of making leather have sufficient rigidity that it would return to its original shape after releasing it, the only thing i would say is that a leather bulb would not snap back to shape instantly like rubber would, it would re-expand out,so it would not be as quick to draw the liquid. but dispensing it would still be the same, might have to be slightly more cautious, and the leather would probably have to run most of the length of the tube to ensure airtightness.
Yep, definitely plausible, but it would likely be a very expensive item for its time.