I'm due August 25th and if I take a childbirth class, I will start it in July. It starts at the beginning of the month and lasts for four weeks, so it'll be done long before my due date. I took a childbirth class at about 6 months with my son and I felt it was too early. So I'm waiting until towards the end this time around. I'll also be taking a breastfeeding class the same month.
I'd suggest that you take the childbirth class in July, that way it won't be too ahead of time and it won't be a last minute deal.