The gal that you're interested in dating is a single mom. You're drawn to her because she is very mature and independent (and beautiful, no doubt)—you like that.
And depending on how you look at it, there may also be some “downsides” when it comes to dating a mom, let alone a single mom.
In my opinion, being a single mother has absolutely nothing to do with one’s marital status.
Heck, there are married women out there that consider themselves single moms within their own household because they assume the majority of the responsibility for their kids.
All relationships have their challenges, especially at the beginning when you are first getting to know each other.
Few people live in isolation and ideally you will have a few dates to get to know the other person, and how you feel about them, before the wider circumstances of their life – like their family, friends, and job – begin to have an impact.