Hello & welcome!
If you have any questions after reading my answer, be sure to let me know.
Talking about the dark circles FIRST
I would like to suggest that a more common reason at 10 months age would be Eye Allergies
as a cause of the dark circles
This is especially important if the baby has a tendency of rubbing the eyes.
I would recommend an eye check up for the same.
Other causes of dark circles include low hemoglobin, vitamin deficiencies, lack of proper sleep, & sometimes these may be hereditary too,
Share your concerns with your pediatrician and discuss all these possibilities,
Eye examination and blood testing may be able to pin point the exact cause of these dark circles,
Coming to the lack of adequate water ....
I would recommend any other non carbonated beverage like a little bit of juice, lime water, coconut water, and fruits that have a high water content (melon, watermelon etc.)