I suggest to book your maternity session for the week 28-32 of your pregnancy as if you leave it for later it would be much harder for you to pose and you will me more tired during the photoshoot. You still can book your session at a later stage, but sooner is the more ideal.
For newborn photography the best time is between 4 and 14 days old to bring your baby to the studio. During the early days babies tend to sleep more and less aware of what is happening around them. They are much more easier to be posed. Some babies still can have bad days, and we might need to call you back for an other day with your newborn.