Okay, here's what I get. I was trying this before with a user created mirror. I replaced it with a Maxis floor mirror and got the option to change the dog's appearance but option 3 where you select the dog collar said I had none. Just to be sure, I sent old Cyd back to the pet store. The dog collar catalog showed the first collar in the wardrobe. I bought a second collar and tried the mirror thing again. It still showed no collars. It is like the toddler clothing thing all over.
Make sure you have the right size collar. I'm pretty sure Cyd has a Small dog so the Large dog collars probably won't fit.