Yes, cats can get depressed.
She will probably feel better when dh is back.
Keep an eye on her food, if cats go too long without eating, they can develop fatty liver disease, which is deadly. But that probably won't happen if she is only feeling bad for too days.
Does she normally eat only dog food, or is she only doing that now because she is depressed? Dog food does not provide enough protein for cats. Cats have a higher protein requirement than dogs.
The protein is worrisome but the biggest thing I would worry about is the lack of taurine...
Taurine is an amino acid that is really important for cats as they have limited means of synthesizing it and they need it for multiple functions of the body. Dogs don't have the same issues, so while cat canned food is supplemented with taurine dog food isn't. Cats that aren't getting enough taurine will develop Feline central retinal degeneration and dilated cardiomyopathy.
Cats really shouldn't be eating dog food - its terrible that she won't eat anything else but have you tried maybe mixing her dog food with some canned cat food and then maybe slowly phasing the dog food out?
Cats are obligate carnivores and dogs aren't - so their diets are vastly different and commercial pet diets reflect that.
As for your original post, sorry your kitty is depressed :-( I think the t-shirt with your DH's smell is a good idea. Good luck!!