Have you considered JavaScript? I know it's not a common answer, but it's VERY easy to get started with (you don't need any compilers or stuff like that) and it's pretty easy to do graphical stuff early on. I've done a bunch of things in JavaScript (note that most require Firefox 1.5, some will work on Firefox 1.0, and a small number will work on other browsers - if you get the "slow script warning" on these, just hit continue a bunch of times):
Nibbles in JS
Missile Command in JS
Robots in JS [warning: VERY addicting to play]
Mario in JS (nowhere near complete)
Brute-forced puzzle solutions (4 dogs start on the corners of a square with side-length 1, each one always runs directly toward the dog counterclockwise from it -- how far do they travel before they meet -- watch the page status bar to see the answer)
Reimplementations of interesting screensavers - every so often, one person (square) randomly picks one of its neighbors, and changes its vote to match that neighbor (3 parties are Democrats, Republicans, Communists in the Linux screensaver this is based on.
Cool mathematical patterns - this one is also based on a Linux screensaver and produces results like
these if you run it long enough.
I even wrote a
simple 3d engine (for the coolest effect, I suggest reducing the quality a few times, picking "Manual Bresenham" and "Filled Polygons")
Starting with an empty HTML file can be difficult, but you could create some wrapper functions for your daughter that save her from writing "document.getElementById()" and setting up the canvas for graphics... I remember when I started learning C in elementary school, my dad wrote a .h file I included that gave me simplified functions to make it simpler to get started.