Good advice there. Although we're very close so she wouldn't tell us not to even if she didn't want us to. But Turkey-and-Football Day is only a few weeks away so we could wait. Mrs. BJC is positively busting at the seams wanting to tell everyone.
Good question...that would be kinda like stealing the thunder of the one getting the baby shower. I guess it depends on how close you are to the cousin...is she going to be thrilled for you? If so, give her the news!
You could mention it to her in private, and get her reaction to it. Then ask her if she would mind you letting the other know.