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.
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:
https://blog.codinghorror.com/modern-logo/
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.
I am exciting to try my own hand at Logo again too with a _bit_ more experience as a programmer than I had back in kindergarten.
I have also been looking at Scratch and at Racket as fun programming sandboxes for learning and playing.
Unfortunately, but actually fortunately, I'm not going to have a computer when I'm talking to them.
Has a 2D physics engine and can use GLB models, among a bunch of other modern features...