Youre an idiot. By introducing the kid early to guys she dates, she is going to continually explain to a crying child why she can't see the male figures in her life, because the chances at 2 months of continuing for years are a lot lower than say 6 months. Now if you're both in agreement that you are meant for each other forever, then I don't see the harm, but OP is clearly not saying that.
And the early part of a relationship should be a bit about you, and whether you think you can truly connect with the other half of it. The kid shouldn't be playing a role in his decision one way or another, at least at this point.
And why the fuck should he not be able to choose how serious a relationship is? Honestly if he just fully commits to playing a dad/husband role, he won't even have a chance to see if he wants that.
Don't listen to this fool, OP. The earlier stages of a real relationship ARE about you. As you move forwards, it becomes more about both of you, but when its still this fresh of a relationship, you need to protect your own interests first. That doesn't mean fuck her over or be an ass, but if having her kid around is keeping you from really evaluating your situation, let her know. And if she can't handle that, she obviously isn't mature enough for a real relationship anyways.