The best time to book your newborn session is actually when you are still pregnant!
The best time to photography the 'newness' of a newborn baby is around the first two weeks of their life when they still 'remember' what it is like in mummy's tummy. This means little time for a new mum to look for a photographer that she likes, particularly when she just has delivered her baby! Often new mums with 3 or 4 weeks old baby come to me in desperation for a newborn booking, and their babies have already changed so much since born.
So, I highly recommend confirming your booking with your preferred photographer when you are 34-36 weeks pregnant. Many photographers offer free consultation, which means you could discuss and be involved in the styling of your newborn shoot.