Is this gift a good idea considering what just happend between us?

I think it's fine because she's just starting seeing another guy. If she was in a serious relationship with another guy then maybe you shouldn't give her a necklace but otherwise I think it's fine. I feel like you might think that giving her this necklace will be the start of something new with her tho and I don't want you to count on that to much. It might but I think chances are it won't. Will you be ok with that if you give her this necklace and nothing comes of it?