I think the driver's ed classes in almost all schools do a disservice to their students by NOT teaching them to drive with a manual transmission. I only know of one that does. It's in a rural setting where fathers need their kids to help out by driving wheat trucks during harvest and so forth.
By all means, teach your daughter to drive one. Not knowing how is akin to being handicapped. I have taught several people to drive manuals. They include three kids, two sisters, and one daughter in law. My neice specifically asked for a manual transmission car so her mother, who refused to EVER learn, would not be able to borrow it from her.
The trick to teaching it is to start out by letting her observe how you do it. She's ridden with you all her life, but probably never REALLY watched what you were doing. Then head to a wide open parking lot, like a school on a Sunday. She won't wear out the clutch on the Yaris in question, unless it's already 99% gone. Go for it. She'll have it down in half an hour.