I don't believe she woke up that morning and said "I think I'll tell Frank Churchill what I suspect about Jane Fairfax and Mr Dixon today". As Robbin said, she acted rather like Miss Bates, who tends to say whatever is uppermost in her mind aloud. Fortunately as Miss Bates loves everybody (we were so informed by the narrator in Chapter 3) she can never be led by this habit into saying something unpleasant about any person. Unfortunately the same cannot be said for Emma.

Matching people fantasies in general are all very well, if kept to oneself, but such fantasies about people (one of them quite unknown to Emma) having adulterous feelings for each other which would betray their respective wife and closest friend, almost a sister, are IMO nasty, unpleasant, and certainly not motivated by any sort of kindness to the object of them. I would not, however, put it so strongly as to say Emma hates Jane Fairfax, since she does show occasional moments of sympathy for her. A pity they don't last.