I'm about to do the same with a 7 year old, I have been thinking that a pillowcase would be our first real project, after doing some test sewing on scraps. I want to teach her how to thread the machine but I'm not going to worry about teaching her how to clean it or change feet or needles yet.
She also has a lot of fairy dolls, so I was thinking if the pillowcase goes well we could do some mini "quilts" for her fairies. (I'm thinking just 2 pieces of fabric "birthed" to make a blanket with some decorative stitches to "quilt" it together - no batting or binding.)