One month old baby and ready to date? I am the single mother of an near nine month old and not ready yet, but I tell you one thing, I AM ready for someone else to be around for support...that is not exactly the best reason to start a relationship though, so you can have a bit of support.
I would suggest she is more interested in security for herself and her child than a love thing, that desire will only last until she feels secure and then she will move on. If you are prepared for that than go for it but don't expect this to be some lifelong thing.
And don't get too attached to the baby.