Toddler teeth brushing

I have a very pleasant 16 month old daughter who becomes a crazed beast whenever you attempt to get a toothbrush in her mouth.  I want to make sure her teeth are clean but it's a constant battle to get her to open her mouth and keep it open.

I've already tried using a warm washcloth and had my finger clamped down on very hard.   I tried to get her to brush my teeth while I did hers and that didn't work.  I also tried to use some baby training toothpaste but she just likes to suck it off.  

I end up letting her hold the brush and she kind of chews on it for a little while but it's clearly not actually cleaning her teeth!

Any suggestions?   Or should I not be so worried about it yet?