Definitely keep the collar, and any other important items like a favorite toy or bone. They will bring you much comfort over the next few years.
This is about your loss, not mine, but maybe what's helped me will also help you: Joe was cremated, and we placed his collar around his urn which sits on the mantle. Every now and then I rub the top of the container like I used to pet him between his ears, and he doesn't feel so gone.
Good luck with the pain; they claim it eventually leaves, and the fond memories stay.