Either marker or fountain pen.
- The marker would be easiest, as she does not load ink.
- Cartridge fountain pens are rather simple to load, I used them in 5th grade. And I use the old Sheaffer calligraphy pens right now, but just casual calligraphy.
I would hold off on the dip pens for later when she gets more into it, as it can get rather messy to use and clean up.
If you would, she can graduate up to the dip pens.
Oooops
But it also depends on what style she wants to learn.
I am starting off with Italic, as I think that it is the easiest. And for that the italic nib fountain pens (Sheaffer, Lamy, Rorting, etc) would do fine. The neat thing about the Sheaffer and Lamy (don't know about the others) is that you can use an ink converter, so you can also use bottle ink, which is MUCH cheaper than cartridge ink, but potentially more messy.
I have an old Sheaffer Calligraphy set that I got at a garage sale, and it does the job for me, for beginning italic.