2 year old and brushing teeth?

I started brushing my daughters teeth when she first got her 2 teeth. I brushed with flouride free toothpaste and now i found out that she has cavities. (shes 2 years old) I started brushing with flouride tooth paste. But i cant get her to spit it out at times, she likes to swallow it at times. But what i want to know is it really bad for her to swallow it.? I use a little tooth paste every time. What can happen if she swallows it?