we have our cat food i the utility room, and when cat was ill, the litter tray went in there too.
We have a door with glass panels between kitchen and utility, and when we got dog, we removed one of the panels, which are abot the size of a cat flap, so the cat can access the utility room and dog can't.
I think that separating the dog from cat food and little is only fair on the cat actually.
Can you put it in the garage/downstairs loo/spare bedroom/bathroom/ and then have stairgate/catflap/hole for cat to enter?
Or just simpler, stairgate on kitchen door and keep dog out?