Yes, the film can be refrigerated, or ideally frozen. If the latter, be sure to bag it properly - I use triple sealing in good Ziplocks. I hope you will be using a frost-free freezer, but a non frost-free is okay with regular checks to ensure humidity doesn't get into the packs. I check my frozen stock monthly and so far all is well.
Refrigerating film is okay for shorter periods. Humidity can be a problem for film in many (especially older) fridges.
I have kept film frozen for 10+ years and even the EI 1600 Fuji rolls were good, showing no fog at all.
You are being very kind to your old canine friend, in his time of need. I commend you for this.