Is my prayer valid after I was touched by the water from a domesticated dog that was walking on water and stopped in the place of my prostration?

Scholars have differed regarding the impurity of the dog, and the most preponderant opinion is that it is impure outwardly and inwardly. So, whatever of its wetness touches you is impure. It would have been incumbent upon you to interrupt your prayer and wash whatever of its wetness touched your body and clothes. However, since you have already completed your prayer while ignorant of the ruling, you are not required to repeat it.