I had my baby shower on Oct 1st and my due date was the 31st... my water broke on the 16th and had my baby girl on the 17th! So you might be cutting it close if your baby decides to come a bit early!
I went to my cousins by marriage the first Sunday in march. Her due date was march 12th. So no. You can have it anytime. It could even be after baby is born. Totally up to you.