Civil Marriage and The Greek Orthodox Church

[weddinggirl19]

My fiance and I are pregnant and due very soon. We do want to marry in the church. However, due to financial issues we wanted to hold off on the big wedding in the church. I was baptized Christian, but he is Greek Orthodox. My question is if we get married at the court house will we be aloud to baptize our new baby? Does is differ according to what the priest/church will allow?