one love- I understand that you have a personal interest in this, having had a child while in undergrad. I had my daughter before I began college, but went through college raising her as a single mom. I advise about adoption simply because I looked into it very seriously and have tremendous respect for adoptive parents and for adoptees and for the whole process. This isn't a judgment statement- I didn't after all choose to adopt out my daughter. But, you make a good point that the OP has already ruled out adoption. Even though I don't buy your point about the importance of "blood". Every adopted child will probably feel rejected at some point from a genetic heritage stance, but being raised in an intact family is an awesome gift to give a child, rare as it is.
JC- maybe you should contact a lawyer and see what is possible. I am totally skeptical about the possibility of drawing up a binding agreement that would keep you geographically located close to her and your child, regardless of if it is YOU who must move 100s or 1000s of miles away for med school education and beyond. I am also skeptical about being able to draw up meaningful child support arrangements at this point. I have heard of it too many times that the mother takes the man back to court to "reassess" the child care needs. Now, I'm in support of the woman getting as much child support as she needs, and I think the woman and child are entitled to quite a bit, but say you graduate from residency with loads of debt. The judge will "consider" that, but would most likely award her a nice monthly increase based on your new monthly income.
Speaking of money, paternity tests in utero are expensive. So are they once the baby's been born. Be diplomatic- I love the idea of checking blood types as a first possible means of determining paternity. You can be totally subtle, then if things don't gel, you could get the test done to make your case. I imagine the mother-to-be has her own health care coverage, so I doubt you'd be hit with that bill, but it would behoove you to go to her pre-natal visits and be a super-supportive guy in the meantime.
Also, for those who say you should go for full custody, good luck! I doubt she would go for that at all. Getting her to give the child your last name would probably be meaningless, too, and her dad would inevitably have something to say about that. These are issues a good lawyer could help you with. But the mommy still has pretty good protection in the courts to keep the child with her at all costs, unless you can prove she's an insane drugged up threat to the child and needs to be jailed.
As far as another man calling your child "Daddy", please understand the context. If you go away to medical school, away to residency, and see your child a few weekends of the year, that may be ALL you can do. I am extremely dubious that she will pick up and follow you as you pursue your degree. So you will have a limited relationship with your child under that scenario, no matter how golden your intentions are right now. What in the world would keep your child from identifying with a step-dad as "Daddy" if you, by virtue of your education and career, were gone most of the time? I can't imagine how painful this would be for you. Entirely hypothetical, of course, but how likely is it that you will be able to do your education, residency training, and career all in the same city where she and your child live. How likely is it that she will pick up and follow you around the country if need be? Do you know her well enough to know that she is so committed to you, the biodad, being a meaningful presence in her child's life that she would disrupt her life so many times to follow you? If she is that committed, go ahead.
Ultimately, I'm not questioning your parenting ability, your desire to be dadddy, or any of that. I'm so very practical with regards to time and location, and the mother's needs and desires which eventually may run counter to yours. Talk to a lawyer, but I doubt there's a way to force her to move whenever you do. I think the judge would see your pursuing a medical career as your choice. So if you were to choose to go to school, you'd choose to leave your child behind and visit when you could.
I do hope that a MAN who has been in your position responds. Single MOMS are different. As the dad, you have much less power and say over day-to-day decisions that will affect your child, even if you are married! Being unmarried, and not in a relationship, I just don't know how many rights you would have.
(my husband and I had a "shotgun wedding," and both his brothers married and shortly thereafter divorced women that they had one-night stands with who ended up pregnant). 
