If they broke up before you and he got together and you were not a factor in their breakup, then you are not a backstabber.
You ARE, on the other hand, a SNEAK; and NOT being a very good friend.
Friends trust each other and are honest with each other. You are weaving an enormous web of lies and deceit that she may never be able to recover from once she catches you at it.
You can fool yourself into thinking you are keeping it a secret for her, but it is really for you. You don't want to feel guilty because you realize that your dating him now will cause her pain.
I'm sorry, but that's the wrong thing to do.
You must be honest with her. I suggest you bring this out in the open. Tell her that you and he like each other, and that you are going to be seeing each other. Tell her that you know she still likes him, and that you don't want to hurt her; but that you don't want to play games and sneak around behind her back, either.
Tell her that you value her friendship, and that's why you're choosing to be honest about what's happening instead of hiding your relationship and letting her find out from someone else.
If she decides not to be friends with you any more, well; that's a risk you'll have to take. If you're lucky, she'll be able to deal with her feelings and the two of you can salvage your friendship.
Meanwhile, if you keep on sneaking around and hiding the fact that that you're now dating her ex from her; and she finds out? I can guarantee your friendship with her will be over for good.
Tell her the truth, and do it now.