If Elizabeth tells either woman (Mrs Gardiner or Charlotte), there is at least a chance that she would tell her husband. Now, Mr Gardiner isn't likely to blab about it, but he might let the secret slip at some point. As for Mr Collins finding out, whoo boy -- that would not be good for Elizabeth.

While there is nobody who needs to know this news, Elizabeth really needs to talk about the proposal and the new information about Wickham's character. She knows that Jane will keep the secret, and Elizabeth knows that Jane will listen sympathetically. Jane is really the only person who meets both of these needs.