Hey, Citygirl!
As you know, I'm in the same boat as you. FYI- I had called the US embassy with a random doubt that I was unable to confirm on their website. In both of our cases, we are US citizens/future moms with Argentine partners/fathers. They did in fact inform me that the father, despite not being a citizen, will have to accompany the US born mother and the child/ren to obtain the dual citizenship that you are applying for.
From what I've researched and read (quite a bit!), it's really straightforward process. It's not just because it's unlike a spousal visa, this is your blood-related direct offspring, and understandably, moreover, considering that in both of our cases, the biological mother is the US citizen, it's as simple as it can possibly get (since proving paternity for a US citizen father can be more questionable at times).
Also, the 5 yrs required for you to have legally resided in the US do NOT have to be consecutive, but 3 of the minimum 5 must have been over the age of 14 yrs.
That's all I know of for now, but for what it's worth, even though you have to set up an appointment beforehand, pay the fees, have all the documents ready and whatnot, in the event that you don't have a particular paper on you or something is not filled out correctly, etc., it's fine, the child legally has up to his/her 18th birthday to claim dual citizenship.
Un beso!