Generally, drooling begins when a child is about 3 months old and lasts till he or she is between 12 and 15 months old, which is also the same time when teething starts. While drooling is a classic symptom of baby's teeth making its way through the gum's surface, drooling doesn't always mean that teething is about to happen. Some experts believe that all this early saliva production or drooling can actually aid babies' digestive systems to develop. So don't worry too much about it :)
My gf's baby girl had her first tooth at 3month old. I was surprised too Coz my boy had his at 7mth. So it does happen, every babies are different. Drooling is normally for baby. Don't worry