Hey, mexjd. I agree with my esteemed colleagues: it is definitely doable. My experience as a new father come law school applicant is that having a child has made me a much more responsible and dedicated person. From what I can tell, both of those qualities will be valuable as a law student and having these experiences will likely make you a stronger applicant, or at least give you a better perspective. I would suggest that you at least have a go at it.
Oh, and congratulations!