Hi T.,
My son is 13 months old, and he uses a little kid toothbrush w/a handle, and not one of the finger brushes. We put him in front of the mirror so he can see what's going on, and we let him "brush" his own teeth first. This usually involves him just chewing on the brush and sort of haphazardly moving it around. After a minute or two, I gently the grab the toothbrush and finish the job.
We do use toothpaste that does not have fluoride in it. We use Nature's Gate Creme De Anise toothpaste. Anise is in black licorice, so it has a very, very mild black licorice taste. (No added sugars.) You could experiment with different toothpastes to see if that helps. Many of the brands geared towards little kids are disgusting; *any* toothpaste w/out fluoride will do at this age, and there are many on the market.
One thought I had was if your daughter might teething now?