Her letter more or less confirms what we'd suspected: she's a member of the Junior Auxiliary. Which means she knows about Terry's wand. And Hermione's wand. And since wands do not materialise out of thin air from their component elements, she knows of the existence of the Order of the Phoenix, if not our full list of activities. Her comment about having friends in common with you suggests that as well, and also suggests that Fred and George were not the only ones who suspected that Molly Weasley was in on the secret, and they may have guessed about Poppy, too, or Pomona, or even Minerva.

AND she knows about your canine ways.

And she's kept it all a secret.

I think you should write to her. Frankly, she's well beyond the point where total secrecy is more of a risk because who even knows what she'll stumble on next? But more than that, I think she's earned a bit of credit. She deserves an acknowledgement. (And an apology, because she's right; you shouldn't have told Harry, not without asking her first. Or at least warning her.)