YANBU to feel upset, confused, and disappointed in the immediate aftermath of this situation.
First, it seems like DD didn't listen at all when you had the initial discussion about the dress. You stressed that it was your favourite and asked her to be especially careful of it; she apparently heard "keep it; I don't want it". She was probably focused on getting the dress as one checklist item in her trip prep, and excited about the trip, and just not listening.
Second, "I thought you didn't want it anymore" is a reasonable explanation for why she left it in her closet until asked for it back rather than laundering and returning it to you promptly, not for selling it without asking you ESPECIALLY as she lives with you so it's no effort at all to check. An explanation that she'd accidentally mixed it up with one of her own dresses she'd meant to sell or that she'd included it by accident in a mixed lot sale or something might have been easier to accept and rationalise. It might still feel bad that she didn't take care of your cherished item you'd entrusted to her, or listen when you asked her to take special care of it, but mistakes happen. This was intentional - definitely not to hurt you or specifically to deprive you of your favourite dress, but to get what she wanted in the short term (money) in complete disregard of your feelings.
Third, she could not have known if it was possible to (almost) replace the dress more than a year after you'd originally bought it. It's a reasonable gamble that she might be able to find it secondhand or (as she did) find a reasonable replacement, but it was far from a sure thing. Just in principle, it was YOUR dress not hers, and if you'd felt that that there was no replacement for the exact item you'd worn on special occasions and had memories attached to, that would have been reasonable of you too no matter how many posters here wouldn't have felt that way and don't understand it. How to dispose of the dress should have been YOUR decision, no one else's.
I would let this go as I don't see much point in discussing it further but I wouldn't lend her anything again and yes, I'm afraid that at least for the short term, I would trust her a little less and think a little less well of her. In the grand scheme of things, though, I think this will seem much less sharp and hurtful in just a little while and things will almost certainly even out over time.