Hello Leameeye14
Yes, this is possible. I suggest you to use the Luggage station to door service.
However, keep in mind that, after the drop-off at Zurich Airport, the luggage will only arrive two days later at your home stay. You might want to take the luggage with you on the train and just send the dog kennel to Randa.
More information: https://sbb-tickets.cc/en/tickets-offers/reservation-luggage/luggage-registration/luggage-station-to-door.html
You can check-inyour luggage here: https://commerce.sbb-tickets.cc/en/luggage.html
Enter 8058 as drop-off point (from) (choose option Zürich-Flughafen, not the option saying Radisson blu), and 3928 as pick-up point (to)
Kind regards,
Roland