I can imagine an 18 year old feeling good enough physically to start classes in 15 days, BUT, I cannot imagine many new mothers, of any age, being able to undertake caring for a newborn without lots of help early on.
Probable scenario is that BHO II was born as much as 3-4 months earlier in either Mercer Island WA (where Stanley Ann attended high school) or more likely in Canada (BC) where there were numerous homes for unwed mothers ala Crittendon.
Frank Davis, close family friend of the senior Dunham, is most probably the father. He left Seattle/Mercer Island a few years before at the request of the local court after facing pedophile (underage girls) allegations. A pregnant Stanley Ann met BHO I at U. of Hawaii and he bought into a deal before their 'marriage' in Mauai and before BHO II's birth. He had nothing to lose and quite possibly thought this would gain him American citizenship. Recall that no one has ever reported seeing the President's parents together, let alone living together.
Although this scenario makes the President a natural born citizen, he is also guilty of a host of misdemeanors or felonies for faking records since the gitgo. Virtually a life a layered frauds since diapers, hence the sealed records, school papers, numerous SS#'s, failure to register for the draft and the yielded law license in Illinois. Who passes the bar as a magna cum laude Harvard Law grad and then turns around and walks away?
She had plenty of friends in the area. She went to high school in the Seattle area (Mercer Island, to be exact), which is about 10 minutes from the Seattle neighborhood (Capital Hill) in which she settled.