Can I channel people’s former pets in the light so they can talk to them?

Yes, indeed this can be done and would be a fine undertaking and use of your talents. You can help the clients who recently contacted you, and you can do this with your own pets as well, and you will see quickly the implications of this for yourself. You can talk not just to the higher self but to the soul extension who was part of your life while in the physical, and this creates the opportunity to recapture the essence of who they were, but informed through higher awareness of their full soul being and with the divine translator provided by Creator to allow communication in human terms.