You really need to be sure of your dates. You're correct in saying that a lot of airlines won't take you at that stage of pregnancy. I think the max limit now is 34/36 weeks. I think at 38 weeks it's a complete refusal to allow you to fly.
What you do also need to look at is whether insurance companies will insure you. Women in the late stages of pregnancy are considered high risk, so insurers are more reluctant to take you. It's not just the health side you need to consider, you wouldn't be able to get insurance for anything - cancellations, theft, etc. If baby did arrive on holiday (the do say 2nd and subsequent babies are often early!), you'd have to decide what you and your family would do. Without insurance if you missed your flight home, you wouldn't be covered so you'd have to cover the cost of that and any subsequent accommodation etc (check what age baby is allowed to fly at), if your family had to leave you to go home, you'd have to deal with this all by yourself while holding the baby too.
What is the cancellation policy of your holiday? What if you have a problem pregnancy and going away is completely out of the question? Is it better to cut your losses early and lose as little money as possible or risk it, pay all your money and hope you have no problems.
As to whether I'd go myself. Remembering how I felt at 38 weeks pregnancy, no I wouldn't. I didn't want to go anywhere other than the hospital to give birth.
Good luck.