You know this may not help but this is what I would do if it were me. I wouldn't push. Pushing can make them rebel more. I would make sure that I brushed my teeth in front of her everytime. I would even do it more than normal just to do it in front of her. Just make sure she sees but don't say a word. Then after a few days or a week, I would conveniently leave the tooth paste and her toothbrush so she could put her own toothpaste on it herself and brush them herself. I wouldn't make a big deal of it... just let her go at her own pace. I give my 1 yr old a toothbrush right now and put toothpaste on it now... just barely enough to see... just so she can get the taste and let her chew on it in the bathtub or during the day... and let her watch me brushing so that when that time comes, I have that covered. But for you..... I would try letting her watch me... even it meant I had to brush 5 times a day. I would probably kind of exaggerate how good that made me feel and then leave hers out to experiment with. If she gets toothpaste on the floor.... no big deal, just buy more and wipe it up. It won't take long and then you can start teaching careful habits of getting the toothpaste out. If you don't want to take it that far, put a very tiny bit on her toothbrush and set it out for her where she can reach it. Let her do it in her own time. That will give her some independence along with "tricking" her into brushing. Usually kids mock what you do. They want to do what you do. Like I said, it may not help but its worth a try. You don't have anything to lose but a messy bathroom floor or sink.
However, if that doesn't work, water has flouride in it and for babies it should be enough right now. Whatever you do, I wouldn't make a big deal of it. That could cause more harm than good.
Let me know if you try it and if it works.
Good Luck, M. T