A lot depends on what you mean by smoking some dog food.
If you mean, take the dog food you have, and put it in the smoker - that
might work - better if it's canned, probably not so much if it's dry.
If you mean ... smoke up some meat and make your own? That's probably the better solution. There's a lot of DIY dog food recipes out there on the 'net, I bet you can find one that your dog would love.
Of course, it would mean that you'd need to smoke something on a regular basis ... (yeah, yeah, twist my arm!)
Let us know what you try!