This question is twofold, as it refers to what age your baby should be for their newborn session, but also at what time in your pregnancy (or after) should you be scheduling it?
The answer to the first question is that every Minneapolis area newborn photographer is going to have a different answer, and depending on the photographer you choose, you may have to abide by their specified window. Some will ONLY work with babies under 10 days old - no matter what. Others will consider an adjusted age (like if baby is born early and needs some extra time in the hospital, etc). Others consider the newborn period to be that first six weeks. I personally prefer working with babies in the 2-3 week range, but will take full term newborns up to 8 weeks for a posed newborn session (with managed expectations) and premature babies much longer.
The truth is, with patience and an understanding of newborns, you have just as good of a chance for a smooth newborn shoot with a six week old baby as you do a one week old baby. The baby in the photo below was 7 weeks old at the time of her session, and while she was much more alert during her awake periods and her session took a bit longer, she still posed like a newborn. We also got some fun awake photos.
My personal preference of 2-3 weeks of age stems from wanting mom and baby to spend that first week resting and bonding with each other, and not spending 4 hours in a photo studio. I know those first few outings with a newborn can be extremely stressful, so take that time with each other, get to that first doctor appointment, and make sure you're on the right track. The other thing, is that with their growth spurts and sleep schedules, that first ten days is usually full of cluster feeding, so if they're exclusively breastfeeding, this usually makes their newborn session creep into the longer end of the spectrum.
As to the second question - when should I be booking my newborn session? - this also is going to vary a lot by photographer. Some photographers consistently book 3-4 months in advance of due dates, so if you are reaching out any later than this, you're out of luck. But that is not every photographer. While I personally DO book some people that far in advance, my general rule of thumb is to book X amount of newborn sessions per month, so that when my moms reach out to say baby has arrived, I have several different dates for her to choose from. That said, I go by due dates, and sometimes I'll literally have 5 babies all born on one day and then a couple born either early or late, so I will end up with extra openings for a last minute booking.
I realize also with the recent recession, a lot of people are waiting on doing newborn photos and deciding after baby arrives if it makes sense for them. I still offer payment plans, and if it makes sense for my schedule, I will gladly say yes after baby has already arrived.