[SyrianHammie]

I would be cautious about having your dog quite so close to your hamster, especially when you aren't in the room. When you are in the room and your dog approaches the cage, keep a close eye out. You said she's a rescue dog which makes me wonder what, if anything, happened to her for her to be in the rescue home? Something could trigger one day which is something I would look out for. Obviously I don't know why your dog was in the rescue home so I might be completely wrong about her. She does seem very sweet though!
In terms of your hamster, keep an eye out for your hamster becoming very stiff when your dog is near the cage. Or your hamster could become startled, jump or even run away and hide under something. If your hamster appears to carry on and acts normally, I wouldn't be too worried about it other than just keeping an eye on it.
Hope this helps!