Nine days and twelve days are not shortly after birth IMO. The mere fact of a birth registration would have generated the birth announcement and at that time a registration of birth could be done on the say of a relative. The fact is the address listed in that birth announcement was NOT associated with the Dunhams or Obama Sr and yet you offer it as proof.
Here is what I found on the Texasdarlin Blog regarding the Obama birth announcement:
3. Although it’s possible that a birth certificate filed by Barack’s grandparents, while he was actually born elsewhere, led to this newspaper announcement, I personally think that’s unlikely because in 1961 these announcements came directly from the Vital Statistics Office as reported by local hospitals, according to the researcher who found this information.
http://texasdarlin.wordpress.com/2008/07/23/obama-was-likely-born-in-hawaii/