I would just go along with your regular relationship.
Do you know why she wanted to break up?

What do you mean she almost broke up with you but decided to go along with it.. ?

I think you should ask her why
she wanted to break up with you,
and what changed her mind.

Other than that, I think you should
follow what she said and don't worry.
Just continue on with the relationship.

It'll be alright

Talk to her. Ask her what was up that she was considering ending it. Was it something you did/said? And if it was something on your part, why did that lead her to wanting to end the relationship altogether?

I'm sure you have nothing to worry about. And it's great that she is honest with you about this. Don't worry, just talk it all out and see what happens. Good luck, man. :]

Sounds very strange, and I would feel the same if i was in your position, you have to find out why, because otherwise you could still be doing something that's making her think to break up with you, and you are unaware of it.
But it's really important you find out, but be careful not to push it, if she dosnt want to talk about it, and you keep pushing it, she might decide to end it after all.
But not matter what from here on out I would try to prepare yourself for the possibility of a break up. Just in case, so you can be ready for it, and help you get on with your life.