Planning to UC in Louisiana
Congratulations on your decision! It's really empowering to realize you can choose not to compromise isn't it?
You can tell your OB you are switching care providers (to yourself, but no need to mention that), or just keep seeing them prenatally then not show up for the birth, if you want just say baby came too fast if they call looking for you. If you keep the Dr. it would make transfer easier if you needed it.
You'll need to contact your local vital statistics office to register the birth, you might get transferred around a while until you find the right person to register an out of hospital birth. Say that specifically, "I need to register an out-of-hospital birth" to get on the right track because getting a copy of the birth cert comes after registration and is more normal for the office to do. Once you get the birth certificate and SSN worked out there should be no problem adding him to insurance. I've birthed out of hospital in KY and PA so I can't help with your state specifically though.
If you want the PKU test done and if your pediatrician can do it, you need to go in for the newborn checkup 1-3 days (24 to 72 hours) from birth. I'm not sure if the filter paper/form is available otherwise in Louisiana to do the test at home if the doc can't, you can try and search from here http://new.dhh.louisiana.gov/index.cfm/page/489 . When you go for the checkup tell the pediatrician it was a home birth, the UC thing need not come up.