I would have done it for a DD of mine, BUT:
The DDs (and DS) all have or had summer jobs and the PO is only open for certain hours daily
The DDs and DS help out at home, do their own laundry, etc.
Give and take is what matters. All give/all take isn't right.
I think you and DD need to sit down and talk when the dust settles on this row. I am guessing that you have argued before about what DD does with her time, or you might not have thought of showing her this thread. I don't think arguing is ever productive when someone clearly has some issues going on.
The problem with making a gesture like this on the spot as it were, as a means of addressing a situation that has been building for a few weeks, is that DD will be too invested in her pov about the parcel and how unreasonable you were, to accept the broader message you are trying to impart here, which is that she needs to show more initiative and take more responsibility for her own chores or tasks that need to get done.
I think you and she both need to step back here. ...gently help her move on in life... Yes, gently is key here, but you won't achieve that by butting heads.
You need to do more 'parenting' and gradually ease her into taking on full responsibility for her life. I don't think you will get anywhere positive by expecting a full fledging just because she has reached a certain age or finished a certain level of education. So make the doctor appointments. Make her a cup of tea or something nice that she likes for dinner.
You and she could meal plan together, work on the house together, cook together, wash up together, do laundry together, and also go out together - to the cinema, to get a facial, to get a lunch out, etc. Above all, prioritise spending time together.
For her part, she needs to commit to getting some chores done daily for you. She also needs to commit to making a list of things she needs to get done (like returning shoes).
*She needs to talk to the doctor when she gets there about the possibility that she is depressed.