Because its edges are stitched I think it's probably vinyl or low-grade leather collar. It looks about 5/8" to 3/4" wide. The rhinestones appear to be all clear, but very reflective (especially in the lab scene). The brass findings behind the stones look similar to "spider settings", but I haven't had any look finding a perfect match. You could use drops of craft paint, miniature brad tacks, something from the hardware store or brass colored scrapbook studs.
They look like they are spaced about an inch apart (from stone to stone) and there are 5 on each side of the brass ring. It buckles in back.
You could easily convert a dog collar, purse strap or belt. Looking at the profile of her neck, it doesn't look like it's very thick.