I told my boss (dissertation advisor) as soon as I got the positive because I wanted him to know the reasons why I was always so tired and kept running to the bathroom. I didn't want him thinking I was shirking my duties when I could no longer pull an all-nighter to do research for him.

And I told my best friend immediately.

Family we told around maybe 8-9 weeks.

General announcement was after the first ultrasound (11 weeks or so).

In your case, I would just tell everyone that, due to some scheduling issues, the wedding date has been changed and you'll let them know when it is later.
God doesn't give special kids to special parents. He takes ordinary, imperfect people, and gifts them with his greatest treasures. And therein, he creates special parents.