It should matter, and it does matter, that she has a child. It's something that should in every case affect your view of the relationship. The thinking is not that since she has a child, you shouldn't be interested in a relationship, but rather that if she has a child you have a responsibility not only to her but to her child as well.
As a single mother, the dating life cannot be easy. She's probably been burned times before, that moment of hesitation was enough for her to question his seriousness and for someone who's most important thing in the world is her child, it's probably not something she can compromise. Good take, author.