I'm 19, I can't be the step-father to a child at this point in my life. Here's why:
Single moms always say they'll take care of the baby all on their own and that you only have to focus on dating the parent, the baby won't even be a problem. However, it ALWAYS turns into focusing on the baby too and the baby WILL turn out to be a problem. I've asked my cousins and other guys who've dated (young) single moms before.
The mom is going to focused on the child no matter what (this is why they always say, "My son is my world"), because duh, she's a mom. Either way, the child is going to be a major part of the relationship no matter what. You'll going to have to watch/take car of the child at some point, even if it's just for a few minutes while she uses the bathroom. If you end up liking/disliking the child, it's also going to have a huge impact on how you see her and how the relationship will go on. She'll probably be tight on money, so she won't be able to go on dates with you often because she can't afford the babysitter. Let's say that something does go wrong, like the baby getting sick and needing doctor's visits/pills, and now she doesn't have enough money for rent/food/whatever this month. What are you going to do? Just let the girl you're dating and her child completely suffer? No, you're probably going to help, even though she said in the beginning she said she didn't need it. Now you're not only tied in financially to the child, you're becoming a parent too.
Lastly, let's say you do grow attached to the child. Maybe you really like being a father and helping take care of the baby. Normally, this would be a good thing for both of you and the child. But what happens if she falls out of love and breaks up with you? Now you'll be dealing with TWO heartbreaks. You're removed from her and a child that you helped care for and have grown to like. That's a really, really shitty feeling that will probably rip out your heart for the next few years. You managed to become single and are no longer a father in one blow.
This is why young guys don't want to date a teen mom, either way things go, it's probably not going to end well for you. I won't even get into the poor life choices argument, it's been said enough.