Eek! No way!
I wouldn't tell anybody still. Even if she gossips, I think it's better to wait and make the announcement according to your own timing and emphasize that you waited to tell until you felt like you were out of the risky window. Really-- let people whisper, if they must, but still take your moment and announce it like it's *your* news to announce, which (of course) it is.
But, eek! Again! You really must be showing! (Soooo cool!)