I don't know why but my elementary school taught my grade of kindergarteners specifically to program using Logo. The class before and after me didn't seem to get this. Some Apple IIe machines that would've quite old by that point and a big room full of kids pair programming Logo. Great memories! And I'm pretty sure this planted the seed that led to my career in software.
My oldest is now in kindergarten and I am going to use Logo to help her learn. I started by buying an Etch-a-sketch that we use together for a real-world point of contact with the idea.
You may find yourself quite surprised, as an adult, by what Logo actually is.
I was never taught much of it, but Logo is massively more sophisticated than most primary education ever gets into -— it's really a multi-paradigm language with quite an elegant loose functional programming style hidden in it.
There's a good article about it here with some links:
Also don't ignore Scratch: if you can teach familiarity in Scratch you are going to set your daughter up really well for all sorts of stuff. Scratch is really Logo's spiritual successor and it's a thing of beauty, IMO.
https://en.wikipedia.org/wiki/Logo_(programming_language)