This sounds like a disaster waiting to happen. You don't sound like you are in the right state of mind to begin an actual relationship, so I am assuming it would just be FWB with this girl. In which case, if you want to pursue, you need to be honest with her and tell her that that is all it is. You're not into her, so by definition you would be using her - if she just wants to use you too, fine, but it needs to be made crystal clear.
Some girls love broken birds, and she may be under some impression that she is going to save you, you'll fall in love with her, she'll heal your wounds, blah blah.....don't play into that. Overall, I would heavily advise against it, especially if you are not even interested in her in the first place. Your girl only broke up with you recently (I assume) and it sounds like it was a rough relationship. You need some time to figure out where you stand and what you want.