Nadine, you don't need to use tooth paste at this stage. Even a clean face washer will do the job of cleaning, but using a little toothbrush is fine too.

I'm not sure why you use glycerine? I'm pretty sure it contains sugar, which is disastrous for teeth. I would definitely give that a miss, and just use the toothbrush with water. When your DD is older you can introduce a children's toothpaste.