My 1 year old daughter has a watering eye, she doesn't have any allergies.

Possibilities: Eyes can water for many reasons. Foreign material has an irritant effect & the eye will try to flush this with tears. The tear duct could be blocked by debris & this be overflow. A new onset infection can cause both watering & pinkeye. You can tru to flush the eye with artificial tears & press on the inner corner of the lower lid over the tear sac. If it persists, see her doc.