Does touching a dog require renewing one's Wudu for Salah?

Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Touching a dog does not nullify one's Wudu (ablution). Thus, whoever touches it while he is in the state of Wudu, his Wudu is valid.
As for the ruling of the impurity of dogs, we have already issued a Fatwa on this issue, for details, please read the Fatwa: 82644.
Allah knows best.