What is the Church’s stand or policy on administering (giving a blessing of healing through the priesthood) to pets?
I know of no place in Church policy or practice that advocates administering to animals. The blessings of the priesthood are given in response to and in accordance with the principle of faith in the Lord Jesus Christ on the part of the one receiving the blessings. The lower forms of creation are not endowed with this lofty principle, so an essential element in priesthood administration would be missing. We can, however, pray to the Lord to invoke his healing powers on any of his creations.