Only thing I can add to what has already been said...you've probably already done this but...
Fire extinguisher(s), and show her how to use one. Make certain the smoke and/or CO2 detectors are up to date and batteries fresh. I don't know if this is a new or old home..but if it's an old home, and have no idea when the detectors were installed- replace them. It's a small price to pay for saving a life.
Most people have them yet never know how, or more importantly when to use a fire extinguisher.It won't put out a building already on fire, but it can stop a small area fire commonly started in the kitchen or bathroom.
3 things that I would add to your very good list are:
Channel Locks 10" or 12" (better yet get both)
Vice Grips
a flat file
Thank you. No I had not thought of this and I am a registered Safety Engineer. One will be bought today. You are correct and I never even thought about one when she moved into her new home.
Get two. One in the Kitchen the other for the bedroom,
Ferril is right. She needs to know how to turn the utilities on and off. And for that she may need a tool to help her turn the water valve on/off at the main. I can barely turn mine. The wife couldn't do it without a T handle that my plumber gave me.
For around the house misc stuff I bought the wife one of those 125 piece $30 household tool kits that comes in a plastic carry case. She's had it for several years. There are 119 pieces that have never been taken out.... but the hammer, screwdriver/bits, pliers, wire cutters and adjustable open end wrench are missing. I'm guessing that's probably what your daughter will find handy too.
If she has a gas water heater long fireplace matches come in handy.
Gardening tools?
Situation: Daughter is unfortunately single and a new homeowner. She lives 20 miles from me.
I'm mystified by the number of people who don't have a bare minimum tool set around...