Few of us believe that kittens don’t need milk as cow’s milk can actually lead to diarrhea.
Try to provide your kitten with a bowl of fresh, clean water at all times. If you doubt that your kitten is not drinking enough, it may result from she has tasted water treatment chemicals in the water. So you can try to provide her filtered or bottled water. Some cats have preference to drink from flowing water sources as they are sensitive to chemicals in the water contained in the bowl and the flowing water remains unpolluted and unprocessed with any chemicals.
Therefore you can purchase water fountains designed especially for cats. But some kittens dislike their whiskers flowing through the side of their water bowl, so another kind of bowl made by different material may help. Don’t forget to provide her plenty of water if she’s eating dry, crunchy kitten food.